eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
451
458
10.15352/aot.1709-1225
53654
Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$
Ahmad Mohammadhasani
a.mohammadhasani53@gmail.com
1
Asma Ilkhanizadeh Manesh
a.ilkhani@vru.ac.ir
2
Rafsanjan University of Vali Asr
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].
http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdf
Linear preserver
right matrix majorization
row stochastic matrix
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
459
472
10.15352/aot.1708-1220
54087
Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces
Mohammad Alomari
mwomath@gmail.com
1
In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .
http://www.aot-math.org/article_54087_0a5c931295412bb7ca2a95f8feda0573.pdf
Hilbert space
selfadjoint operators
h-synchronization
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
473
490
10.15352/aot.1708-1215
54270
Perturbation of minimum attaining operators
Jadav Ganesh
ma12p1003@iith.ac.in
1
Golla Ramesh
rameshg@iith.ac.in
2
Daniel Sukumar
suku@iith.ac.in
3
Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist), Telangana 502285, India
IIT Hyderabad
Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist), Telangana 502285, India
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.
http://www.aot-math.org/article_54270_bc17d5d42fb655dade72954a6c56fd0a.pdf
minimum modulus
spectrum
essential spectrum
porous set
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
491
506
10.15352/aot.1711-1257
54492
Besicovitch almost automorphic solutions of nonautonomous differential equations of first order
Marko Kostic
marco.s@verat.net
1
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.
http://www.aot-math.org/article_54492_65ee01700cc48f0cf7bef87718a3f617.pdf
Besicovitch almost automorphic functions
weighted Besicovitch pseudo-almost automorphic functions
nonautonomous differential equations of first order
evolution systems
Green's functions
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
507
521
10.15352/aot.1712-1270
56029
A Kakutani-Mackey-like theorem
Marina Haralampidou
mharalam@math.uoa.gr
1
Konstantinos Tzironis
tzirk@math.uoa.gr
2
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
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.
http://www.aot-math.org/article_56029_e54f74797c92d1f650c19dab2b77f90e.pdf
(semi-)quasi-complemented linear space
quasi-complementor
pseudo-$H$-space
automorphically perfect pair
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
522
537
10.15352/aot.1709-1236
57072
$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application
Fanghui Liao
liaofanghui1028@163.com
1
Zongguang Liu
liuzg@cumtb.edu.cn
2
Hongbin Wang
hbwang_2006@163.com
3
China University of Mining and Technology(Beijing)
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.
http://www.aot-math.org/article_57072_888f8c2b8da0ea7fac2ff9eeb211dc2a.pdf
T1 theorem
Triebel-Lizorkin space
Besov space
RD-space
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
538
550
10.15352/aot.1710-1244
57403
Fixed points of a class of unitary operators
Namita Das
namitadas440@yahoo.co.in
1
Jitendra Behera
jitendramath0507@gmail.com
2
P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
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.
http://www.aot-math.org/article_57403_9ef2e37b57c571444740ffc979926104.pdf
Right half plane
Bergman space
unitary operator
automorphism
fixed point
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
551
581
10.15352/aot.1709-1227
57444
Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with critical exponential growth
Hanen Hezzi
hezzihanen81@gmail.com
1
University of Tunis El Manar, Faculty of Sciences of Tunis, LR03ES04 partial differential equations and applications, 2092 Tunis, Tunisia
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.
http://www.aot-math.org/article_57444_2c0e0da5d64c8fabde55e8ee06badb79.pdf
Nonlinear Schrodinger system
global well-posedness
scattering
blow-up
Moser-Trudinger inequality
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
582
605
10.15352/aot.1801-1297
57481
Closedness and invertibility for the sum of two closed operators
Nikolaos Roidos
nikolaosroidos@gmail.com
1
Institute of Analysis, Leibniz University of Hanover, Germany
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.
http://www.aot-math.org/article_57481_9dc50d9f66c3c3266ee8dd0c78d135ef.pdf
Sectorial operators
bounded $H^{infty}$-calculus
maximal regularity
abstract Cauchy problem
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
606
619
10.15352/aot.1710-1246
57735
Parallel iterative methods for solving the common null point problem in Banach spaces
Tuyen Truong
tuyentm@tnus.edu.vn
1
Nguyen Trang
nguyenminhtrang@tnut.edu.vn
2
Department of Mathematics and Informatics, Thainguyen University of Sciences, Thai Nguyen, Vietnam
Faculty of International training, Thainguyen University of Technology, Thai Nguyen, Vietnam
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.
http://www.aot-math.org/article_57735_78e447c015a1cc99204e72dafc32433e.pdf
Common null point problem
maximal monotone operator
generalized resolvent
$varepsilon$-enlargement
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
620
631
10.15352/aot.1712-1267
57759
Complex isosymmetric operators
Muneo Chō
chiyom01@kanagawa-u.ac.jp
1
Ji Eun Lee
jieunlee7@sejong.ac.kr
2
T. Prasad
prasadvalapil@gmail.com
3
Kôtarô Tanahashi
tanahasi@tohoku-mpu.ac.jp
4
Kanagawa University
Department of Mathematics and Statistics, Sejong University, Seoul 143-747, Korea
Department of Mathematics, Cochin university of Science and Technology, Kochi, India
Department of Mathematics, Tohoku Medical and Pharmaceutical University, Sendai 981-8558, Japan
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.
http://www.aot-math.org/article_57759_b9d4decc8062d9cb38ddba2ce3edb0bc.pdf
Isosymmetric operator
complex isosymmetric operator
complex symmetric operator
(m
C)-isometric operator
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
632
638
10.15352/aot.1711-1259
58027
Variant versions of the Lewent type determinantal inequality
Ali Morassaei
morassaei@znu.ac.ir
1
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.
http://www.aot-math.org/article_58027_e4993959d2838f85d7a990cb957c644c.pdf
Lewent inequality
determinantal inequality
Jensen-Mercer inequality
trace class operators
contraction
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
639
646
10.15352/aot.1801-1295
58068
wUR modulus and normal structure in Banach spaces
Ji Gao
jgao@ccp.edu
1
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.
http://www.aot-math.org/article_58068_bab5247b1aec6e648c85b7d2223d9400.pdf
uniform convexity
normal structure
wUR
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
647
654
10.15352/aot.1801-1288
58111
The matrix power means and interpolations
DINH Trung Hoa
trunghoa.math@gmail.com
1
Raluca Dumitru
raluca.dumitru@unf.edu
2
Jose A. Franco
jose.franco@unf.edu
3
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.
http://www.aot-math.org/article_58111_2db06770ff58292e14a48df88a3e8429.pdf
Kubo-Ando means
Interpolation
arithmetic mean
geometric mean
harmonic mean
Heron means
Heinz means
power means
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
655
681
10.15352/aot.1710-1241
58258
$C^*$-algebra distance filters
Tristan Bice
tristan.bice@gmail.com
1
Alessandro Vignati
ale.vignati@gmail.com
2
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.
http://www.aot-math.org/article_58258_60253d2648889c6465fbb303065fad63.pdf
filter
$C^*$-algebra
compact projection
non-symmetric distance
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
682
689
10.15352/aot.1711-1262
58259
On Neugebauer's covering theorem
Jésus M. Aldaz
jesus.munarriz@uam.es
1
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.
http://www.aot-math.org/article_58259_27f6aa7b3ddc36299f175589a7784c20.pdf
Uncentered maximal operator
restricted weak type
geometrically doubling
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
690
698
10.15352/aot.1802-1316
58113
The existence of hyper-invariant subspaces for weighted shift operators
Hossein Sadeghi
hsadeghi@znu.ac.ir
1
Farzollah Mirzapour
f.mirza@znu.ac.ir
2
University of Zanjan
University of Zanjan
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.
http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdf
invariant subspace
weighted space
shift operator
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
699
709
10.15352/aot.1712-1268
58482
Orthogonality of bounded linear operators on complex Banach spaces
Kallol Paul
kalloldada@gmail.com
1
Debmalya Sain
saindebmalya@gmail.com
2
Arpita Mal
arpitamalju@gmail.com
3
Kalidas Mandal
kalidas.mandal14@gmail.com
4
Department of Mathematics Jadavpur University Kolkata 700032 India
Indian Institute of Science, Bengaluru
Department of Mathematics Jadavpur University Kolkata 700032 India
Department of Mathematics Jadavpur University Kolkata 700032 India
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.
http://www.aot-math.org/article_58482_7dbaeeafc2780dac3d0996c2d9a48612.pdf
Birkhoff-James orthogonality
complex Banach space
bounded linear operator
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
710
730
10.15352/aot.1801-1298
60104
Affine actions and the Yang-Baxter equation
Dilian Yang
dyang@uwindsor.ca
1
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.
http://www.aot-math.org/article_60104_5b1e93d062f80db45bd3e9f530226155.pdf
Yang-Baxter equation
set-theoretic solution
affine action
C*-dynamical system
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2018-07-01
3
3
731
744
10.15352/aot.1804-1343
60341
Characterizing projections among positive operators in the unit sphere
Antonio Peralta
aperalta@ugr.es
1
Universidad de Granada
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.
http://www.aot-math.org/article_60341_1b13a753583eb613f2eecd19bf0bb7e9.pdf
Projection
unit sphere around a subset
bounded linear operator
compact linear operator