Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$
451
458
EN
Ahmad
Mohammadhasani
a.mohammadhasani53@gmail.com
Asma
Ilkhanizadeh Manesh
Rafsanjan University of Vali Asr
a.ilkhani@vru.ac.ir
10.15352/aot.1709-1225
A nonnegative real matrix $Rin textbf{M}_{n,m}$ with the property that all its row sums are one is said to be row stochastic. For $x, y in mathbb{R}_{n}$, we say $x$ is right matrix majorized by $y$ (denoted by $xprec_{r} y$) if there exists an $n$-by-$n$ row stochastic matrix $R$ such that $x=yR$. The relation $sim_{r}$ on $mathbb{R}_{n}$ is defined as follows. $xsim_{r}y$ if and only if $ xprec_{r} yprec_{r} x$. In the present paper, we characterize the linear preservers of $sim_{r}$ on $mathbb{R}_{n}$, and answer the question raised by F. Khalooei [Wavelet Linear Algebra textbf{1} (2014), no. 1, 43--50].
Linear preserver,right matrix majorization,row stochastic matrix
http://www.aot-math.org/article_53654.html
http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces
459
472
EN
Mohammad
Alomari
mwomath@gmail.com
10.15352/aot.1708-1220
In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .
Hilbert space,selfadjoint operators,h-synchronization
http://www.aot-math.org/article_54087.html
http://www.aot-math.org/article_54087_0a5c931295412bb7ca2a95f8feda0573.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Perturbation of minimum attaining operators
473
490
EN
Jadav
Ganesh
Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist),
Telangana 502285, India
ma12p1003@iith.ac.in
Golla
Ramesh
IIT Hyderabad
rameshg@iith.ac.in
Daniel
Sukumar
Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist),
Telangana 502285, India
suku@iith.ac.in
10.15352/aot.1708-1215
We prove that the minimum attaining property of a bounded linear operator on a Hilbert space $H$ whose minimum modulus lies in the discrete spectrum, is stable under small compact perturbations. We also observe that given a bounded operator with strictly positive essential minimum modulus, the set of compact perturbations which fail to produce a minimum attaining operator is smaller than a nowhere dense set. In fact it is a porous set in the ideal of all compact operators on $H$. Further, we try to extend these stability results to perturbations by all bounded linear operators with small norm and obtain subsequent results.
minimum modulus,spectrum,essential spectrum,porous set
http://www.aot-math.org/article_54270.html
http://www.aot-math.org/article_54270_bc17d5d42fb655dade72954a6c56fd0a.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Besicovitch almost automorphic solutions of nonautonomous differential equations of first order
491
506
EN
Marko
Kostic
marco.s@verat.net
10.15352/aot.1711-1257
The main purpose of this paper is to analyze the existence and uniqueness of Besicovitch almost automorphic solutions and weighted Besicovitch pseudo-almost automorphic solutions of nonautonomous differential equations of first order. We provide an interesting application of our abstract theoretical results.
Besicovitch almost automorphic functions,weighted Besicovitch pseudo-almost automorphic functions,nonautonomous differential equations of first order,evolution systems,Green's functions
http://www.aot-math.org/article_54492.html
http://www.aot-math.org/article_54492_65ee01700cc48f0cf7bef87718a3f617.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
A Kakutani-Mackey-like theorem
507
521
EN
Marina
Haralampidou
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
mharalam@math.uoa.gr
Konstantinos
Tzironis
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
tzirk@math.uoa.gr
10.15352/aot.1712-1270
We give a partial extension of a Kakutani-Mackey theorem for quasi-complemented vector spaces. This can be applied in the representation theory of certain complemented (non-normed) topological algebras. The existence of continuous linear maps, in the context of quasi-complemented vector spaces, is a very important issue in their study. Relative to this, we prove that every Hausdorff quasi-complemented locally convex space has continuous linear maps, under which a certain quasi-complemented locally convex space, turns to be pre-Hilbert.
(semi-)quasi-complemented linear space,quasi-complementor,pseudo-$H$-space,automorphically perfect pair
http://www.aot-math.org/article_56029.html
http://www.aot-math.org/article_56029_e54f74797c92d1f650c19dab2b77f90e.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application
522
537
EN
Fanghui
Liao
liaofanghui1028@163.com
Zongguang
Liu
China University of Mining and Technology(Beijing)
liuzg@cumtb.edu.cn
Hongbin
Wang
hbwang_2006@163.com
10.15352/aot.1709-1236
Using Calder'{o}n's reproducing formulas and almost orthogonal estimates, the $T1$ theorem for the inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces is obtained. As an application, new characterizations for these spaces with ``half" the usual conditions of the approximate to the identity are presented.
T1 theorem,Triebel-Lizorkin space,Besov space,RD-space
http://www.aot-math.org/article_57072.html
http://www.aot-math.org/article_57072_888f8c2b8da0ea7fac2ff9eeb211dc2a.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Fixed points of a class of unitary operators
538
550
EN
Namita
Das
P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
namitadas440@yahoo.co.in
Jitendra
Behera
P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
jitendramath0507@gmail.com
10.15352/aot.1710-1244
In this paper, we consider a class of unitary operators defined on the Bergman space of the right half plane and characterize the fixed points of these unitary operators. We also discuss certain intertwining properties of these operators. Applications of these results are also obtained.
Right half plane,Bergman space,unitary operator,automorphism,fixed point
http://www.aot-math.org/article_57403.html
http://www.aot-math.org/article_57403_9ef2e37b57c571444740ffc979926104.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with critical exponential growth
551
581
EN
Hanen
Hezzi
University of Tunis El Manar, Faculty of Sciences of Tunis, LR03ES04 partial differential equations and applications, 2092 Tunis, Tunisia
hezzihanen81@gmail.com
10.15352/aot.1709-1227
The initial value problem for some coupled nonlinear Schrodinger equations in two space dimensions with exponential growth is investigated. In the defocusing case, global well-posedness and scattering are obtained. In the focusing sign, global and non global existence of solutions are discussed via potential well- method.
Nonlinear Schrodinger system,global well-posedness,scattering,blow-up,Moser-Trudinger inequality
http://www.aot-math.org/article_57444.html
http://www.aot-math.org/article_57444_2c0e0da5d64c8fabde55e8ee06badb79.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Closedness and invertibility for the sum of two closed operators
582
605
EN
Nikolaos
Roidos
Institute of Analysis, Leibniz University of Hanover, Germany
nikolaosroidos@gmail.com
10.15352/aot.1801-1297
We show a Kalton--Weis type theorem for the general case of non-commuting operators. More precisely, we consider sums of two possibly non-commuting linear operators defined in a Banach space such that one of the operators admits a bounded $H^infty$-calculus, the resolvent of the other one satisfies some weaker boundedness condition and the commutator of their resolvents has certain decay behavior with respect to the spectral parameters. Under this consideration, we show that the sum is closed and that after a sufficiently large positive shift it becomes invertible, and moreover sectorial. As an application we recover a classical result on the existence, uniqueness and maximal $L^{p}$-regularity for solutions of the abstract linear non-autonomous parabolic problem.
Sectorial operators,bounded $H^{infty}$-calculus,maximal regularity,abstract Cauchy problem
http://www.aot-math.org/article_57481.html
http://www.aot-math.org/article_57481_9dc50d9f66c3c3266ee8dd0c78d135ef.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Parallel iterative methods for solving the common null point problem in Banach spaces
606
619
EN
Tuyen
Truong
Department of Mathematics and Informatics, Thainguyen University of Sciences, Thai Nguyen, Vietnam
tuyentm@tnus.edu.vn
Nguyen
Trang
Faculty of International training, Thainguyen University of Technology, Thai Nguyen, Vietnam
nguyenminhtrang@tnut.edu.vn
10.15352/aot.1710-1246
We consider the common null point problem in Banach spaces. Then, using the hybrid projection method and the $varepsilon $- enlargement of maximal monotone operators, we prove two strong convergence theorems for finding a solution of this problem.
Common null point problem,maximal monotone operator,generalized resolvent,$varepsilon$-enlargement
http://www.aot-math.org/article_57735.html
http://www.aot-math.org/article_57735_78e447c015a1cc99204e72dafc32433e.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Complex isosymmetric operators
620
631
EN
Muneo
Chō
Kanagawa University
chiyom01@kanagawa-u.ac.jp
Ji Eun
Lee
Department of Mathematics and Statistics, Sejong University, Seoul 143-747, Korea
jieunlee7@sejong.ac.kr
T.
Prasad
Department of Mathematics, Cochin university of Science and Technology, Kochi, India
prasadvalapil@gmail.com
Kôtarô
Tanahashi
Department of Mathematics, Tohoku Medical and Pharmaceutical University, Sendai 981-8558, Japan
tanahasi@tohoku-mpu.ac.jp
10.15352/aot.1712-1267
In this paper, we introduce complex isosymmetric and $(m,n,C)$-isosymmetric operators on a Hilbert space $mathcal H$ and study properties of such operators. In particular, we prove that if $T in {mathcal B}(mathcal H)$ is an $(m,n,C)$-isosymmetric operator and $N$ is a $k$-nilpotent operator such that $T$ and $N$ are $C$-doubly commuting, then $T + N$ is an $(m+2k-2, n+2k-1,C)$-isosymmetric operator. Moreover, we show that if $T$ is $(m,n,C)$-isosymmetric and if $S$ is $(m',D)$-isometric and $n'$-complex symmetric with a conjugation $D$, then $T otimes S$ is $(m+m'-1,n+n'-1,C otimes D)$-isosymmetric.
Isosymmetric operator,complex isosymmetric operator,complex symmetric operator,(m,C)-isometric operator
http://www.aot-math.org/article_57759.html
http://www.aot-math.org/article_57759_b9d4decc8062d9cb38ddba2ce3edb0bc.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Variant versions of the Lewent type determinantal inequality
632
638
EN
Ali
Morassaei
morassaei@znu.ac.ir
10.15352/aot.1711-1259
In this paper, we present a refinement of the Lewent determinantal inequality and then, we show that the following inequality holds begin{align*} &detfrac{I_{mathcal{H}}+A_1}{I_{mathcal{H}}-A_1}+detfrac{I_{mathcal{H}}+A_n}{I_{mathcal{H}}-A_n}-sum_{j=1}^nlambda_j detleft(frac{I_{mathcal{H}}+A_j}{I_{mathcal{H}}-A_j}right)\ & ge detleft[left(frac{I_{mathcal{H}}+A_1}{I_{mathcal{H}}-A_1}right)left(frac{I_{mathcal{H}}+A_n}{I_{mathcal{H}}-A_n}right)prod_{j=1}^n left(frac{I_{mathcal{H}}+A_j}{I_{mathcal{H}}-A_j}right)^{-lambda_j}right],, end{align*} where $A_jinmathbb{B}(mathcal{H})$, $0le A_j < I_mathcal{H}$, $A_j's$ are trace class operators and $A_1 le A_j le A_n~(j=1,cdots,n)$ and $sum_{j=1}^nlambda_j=1,~ lambda_j ge 0~ (j=1,cdots,n)$. In addition, we present some new versions of the Lewent type determinantal inequality.
Lewent inequality,determinantal inequality,Jensen-Mercer inequality,trace class operators,contraction
http://www.aot-math.org/article_58027.html
http://www.aot-math.org/article_58027_e4993959d2838f85d7a990cb957c644c.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
wUR modulus and normal structure in Banach spaces
639
646
EN
Ji
Gao
jgao@ccp.edu
10.15352/aot.1801-1295
Let $X$ be a Banach space. In this paper, we study the properties of wUR modulus of $X$, $delta_X(varepsilon, f),$ where $0 le varepsilon le 2$ and $f in S(X^*),$ and the relationship between the values of wUR modulus and reflexivity, uniform non-squareness and normal structure respectively. Among other results, we proved that if $ delta_X(1, f)> 0$ for any $fin S(X^*),$ then $X$ has weak normal structure.
uniform convexity,normal structure,wUR
http://www.aot-math.org/article_58068.html
http://www.aot-math.org/article_58068_bab5247b1aec6e648c85b7d2223d9400.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
The matrix power means and interpolations
647
654
EN
DINH
Trung Hoa
trunghoa.math@gmail.com
Raluca
Dumitru
raluca.dumitru@unf.edu
Jose A.
Franco
jose.franco@unf.edu
10.15352/aot.1801-1288
It is well-known that the Heron mean is a linear interpolation between the arithmetic and the geometric means while the matrix power mean $P_t(A,B):= A^{1/2}left(frac{I+(A^{-1/2}BA^{-1/2})^t}{2}right)^{1/t}A^{1/2}$ interpolates between the harmonic, the geometric, and the arithmetic means. In this article, we establish several comparisons between the matrix power mean, the Heron mean and the Heinz mean. Therefore, we have a deeper understanding about the distribution of these matrix means.
Kubo-Ando means,Interpolation,arithmetic mean,geometric mean,harmonic mean,Heron means,Heinz means,power means
http://www.aot-math.org/article_58111.html
http://www.aot-math.org/article_58111_2db06770ff58292e14a48df88a3e8429.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
$C^*$-algebra distance filters
655
681
EN
Tristan
Bice
tristan.bice@gmail.com
Alessandro
Vignati
ale.vignati@gmail.com
10.15352/aot.1710-1241
We use non-symmetric distances to give a self-contained account of $C^*$-algebra filters and their corresponding compact projections, simultaneously simplifying and extending their general theory.
filter,$C^*$-algebra,compact projection,non-symmetric distance
http://www.aot-math.org/article_58258.html
http://www.aot-math.org/article_58258_60253d2648889c6465fbb303065fad63.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
On Neugebauer's covering theorem
682
689
EN
Jésus M.
Aldaz
jesus.munarriz@uam.es
10.15352/aot.1711-1262
We present a new proof of a covering theorem of C. J. Neugebauer, stated in a slightly more general form than the original version; we also give an application to restricted weak type (1,1) inequalities for the uncentered maximal operator.
Uncentered maximal operator,restricted weak type,geometrically doubling
http://www.aot-math.org/article_58259.html
http://www.aot-math.org/article_58259_27f6aa7b3ddc36299f175589a7784c20.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
The existence of hyper-invariant subspaces for weighted shift operators
690
698
EN
Hossein
Sadeghi
University of Zanjan
hsadeghi@znu.ac.ir
Farzollah
Mirzapour
University of Zanjan
f.mirza@znu.ac.ir
10.15352/aot.1802-1316
We introduce some classes of Banach spaces for which the hyperinvariant subspace problem for the shift operator has positive answer. Moreover, we provide sufficient conditions on weights which ensure that certain subspaces of $ell^2_{{beta}}(mathbb{Z})$ are closed under convolution. Finally we consider some cases of weighted spaces for which the problem remains open.
invariant subspace,weighted space,shift operator
http://www.aot-math.org/article_58113.html
http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Orthogonality of bounded linear operators on complex Banach spaces
699
709
EN
Kallol
Paul
Department of Mathematics
Jadavpur University
Kolkata 700032
India
kalloldada@gmail.com
Debmalya
Sain
Indian Institute of Science, Bengaluru
saindebmalya@gmail.com
Arpita
Mal
Department of Mathematics
Jadavpur University
Kolkata 700032
India
arpitamalju@gmail.com
Kalidas
Mandal
Department of Mathematics
Jadavpur University
Kolkata 700032
India
kalidas.mandal14@gmail.com
10.15352/aot.1712-1268
We study Birkhoff-James orthogonality of compact linear operators on complex reflexive Banach spaces and obtain its characterization. By means of introducing new definitions, we illustrate that it is possible in the complex case, to develop a study of orthogonality of compact linear operators, analogous to the real case. Furthermore, earlier operator theoretic characterizations of Birkhoff-James orthogonality in the real case, can be obtained as simple corollaries to our present study. In fact, we obtain more than one equivalent characterizations of Birkhoff-James orthogonality of compact linear operators in the complex case, in order to distinguish the complex case from the real case.
Birkhoff-James orthogonality,complex Banach space,bounded linear operator
http://www.aot-math.org/article_58482.html
http://www.aot-math.org/article_58482_7dbaeeafc2780dac3d0996c2d9a48612.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Affine actions and the Yang-Baxter equation
710
730
EN
Dilian
Yang
dyang@uwindsor.ca
10.15352/aot.1801-1298
In this paper, the relations between the Yang-Baxter equation and affine actions are explored in detail. In particular, we classify the injective set-theoretic solutions of the Yang-Baxter equation in two ways: (i) by their associated affine actions of their structure groups on their derived structure groups, and (ii) by the $C^*$-dynamical systems obtained from their associated affine actions. On the way to our main results, several other useful results are also obtained.
Yang-Baxter equation,set-theoretic solution,affine action,C*-dynamical system
http://www.aot-math.org/article_60104.html
http://www.aot-math.org/article_60104_5b1e93d062f80db45bd3e9f530226155.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
3
2018
07
01
Characterizing projections among positive operators in the unit sphere
731
744
EN
Antonio
Peralta
0000-0003-2528-8357
Universidad de Granada
aperalta@ugr.es
10.15352/aot.1804-1343
Let $E$ and $P$ be subsets of a Banach space $X$, and let us define the unit sphere around $E$ in $P$ as the set $$Sph(E;P) :=left{ xin P : |x-b|=1 hbox{ for all } bin E right}.$$ Given a $C^*$-algebra $A$ and a subset $Esubset A,$ we shall write $Sph^+ (E)$ or $Sph_A^+ (E)$ for the set $Sph(E;S(A^+)),$ where $S(A^+)$ denotes the unit sphere of $A^+$. We prove that, for every complex Hilbert space $H$, the following statements are equivalent for every positive element $a$ in the unit sphere of $B(H)$: (a) $a$ is a projection (b) $Sph^+_{B(H)} left( Sph^+_{B(H)}({a}) right) ={a}$. We also prove that the equivalence remains true when $B(H)$ is replaced with an atomic von Neumann algebra or with $K(H_2)$, where $H_2$ is an infinite-dimensional and separable complex Hilbert space. In the setting of compact operators we establish a stronger conclusion by showing that the identity $$Sph^+_{K(H_2)} left( Sph^+_{K(H_2)}(a) right) =left{ bin S(K(H_2)^+) : !! begin{array}{c}s_{_{K(H_2)}} (a) leq s_{_{K(H_2)}} (b), hbox{ and }\ textbf{1}-r_{_{B(H_2)}}(a)leq textbf{1}-r_{_{B(H_2)}}(b) end{array}right},$$ holds for every $a$ in the unit sphere of $K(H_2)^+$, where $r_{_{B(H_2)}}(a)$ and $s_{_{K(H_2)}} (a)$ stand for the range and support projections of $a$ in $B(H_2)$ and $K(H_2)$, respectively.
Projection,unit sphere around a subset,bounded linear operator,compact linear operator
http://www.aot-math.org/article_60341.html
http://www.aot-math.org/article_60341_1b13a753583eb613f2eecd19bf0bb7e9.pdf