Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$
Ahmad
Mohammadhasani
author
Asma
Ilkhanizadeh Manesh
Rafsanjan University of Vali Asr
author
text
article
2018
eng
A nonnegative real matrix $R\in \textbf{M}_{n,m}$ 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 $x\prec_{r} y$) 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. $x\sim_{r}y$ if and only if $ x\prec_{r} y\prec_{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].
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
451
458
http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdf
dx.doi.org/10.15352/aot.1709-1225
Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces
Mohammad
Alomari
author
text
article
2018
eng
In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
459
472
http://www.aot-math.org/article_54087_0a5c931295412bb7ca2a95f8feda0573.pdf
dx.doi.org/10.15352/aot.1708-1220
Perturbation of minimum attaining operators
Jadav
Ganesh
Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist),
Telangana 502285, India
author
Golla
Ramesh
IIT Hyderabad
author
Daniel
Sukumar
Department of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist),
Telangana 502285, India
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
473
490
http://www.aot-math.org/article_54270_bc17d5d42fb655dade72954a6c56fd0a.pdf
dx.doi.org/10.15352/aot.1708-1215
Besicovitch almost automorphic solutions of nonautonomous differential equations of first order
Marko
Kostic
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
491
506
http://www.aot-math.org/article_54492_65ee01700cc48f0cf7bef87718a3f617.pdf
dx.doi.org/10.15352/aot.1711-1257
A Kakutani-Mackey-like theorem
Marina
Haralampidou
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
author
Konstantinos
Tzironis
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
507
521
http://www.aot-math.org/article_56029_e54f74797c92d1f650c19dab2b77f90e.pdf
dx.doi.org/10.15352/aot.1712-1270
$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application
Fanghui
Liao
author
Zongguang
Liu
China University of Mining and Technology(Beijing)
author
Hongbin
Wang
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
522
537
http://www.aot-math.org/article_57072_888f8c2b8da0ea7fac2ff9eeb211dc2a.pdf
dx.doi.org/10.15352/aot.1709-1236
Fixed points of a class of unitary operators
Namita
Das
P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
author
Jitendra
Behera
P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
538
550
http://www.aot-math.org/article_57403_9ef2e37b57c571444740ffc979926104.pdf
dx.doi.org/10.15352/aot.1710-1244
Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with critical exponential growth
Hanen
Hezzi
University of Tunis El Manar, Faculty of Sciences of Tunis, LR03ES04 partial differential equations and applications, 2092 Tunis, Tunisia
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
551
581
http://www.aot-math.org/article_57444_2c0e0da5d64c8fabde55e8ee06badb79.pdf
dx.doi.org/10.15352/aot.1709-1227
Closedness and invertibility for the sum of two closed operators
Nikolaos
Roidos
Institute of Analysis, Leibniz University of Hanover, Germany
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
582
605
http://www.aot-math.org/article_57481_9dc50d9f66c3c3266ee8dd0c78d135ef.pdf
dx.doi.org/10.15352/aot.1801-1297
Parallel iterative methods for solving the common null point problem in Banach spaces
Tuyen
Truong
Department of Mathematics and Informatics, Thainguyen University of Sciences, Thai Nguyen, Vietnam
author
Nguyen
Trang
Faculty of International training, Thainguyen University of Technology, Thai Nguyen, Vietnam
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
606
619
http://www.aot-math.org/article_57735_78e447c015a1cc99204e72dafc32433e.pdf
dx.doi.org/10.15352/aot.1710-1246
Complex isosymmetric operators
Muneo
Chō
Kanagawa University
author
Ji Eun
Lee
Department of Mathematics and Statistics, Sejong University, Seoul 143-747, Korea
author
T.
Prasad
Department of Mathematics, Cochin university of Science and Technology, Kochi, India
author
Kôtarô
Tanahashi
Department of Mathematics, Tohoku Medical and Pharmaceutical University, Sendai 981-8558, Japan
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
620
631
http://www.aot-math.org/article_57759_b9d4decc8062d9cb38ddba2ce3edb0bc.pdf
dx.doi.org/10.15352/aot.1712-1267
Variant versions of the Lewent type determinantal inequality
Ali
Morassaei
author
text
article
2018
eng
In this paper, we present a refinement of the Lewent determinantal inequality and then, we show that the following inequality holds \begin{align*} &\det\frac{I_{\mathcal{H}}+A_1}{I_{\mathcal{H}}-A_1}+\det\frac{I_{\mathcal{H}}+A_n}{I_{\mathcal{H}}-A_n}-\sum_{j=1}^n\lambda_j \det\left(\frac{I_{\mathcal{H}}+A_j}{I_{\mathcal{H}}-A_j}\right)\\ & \ge \det\left[\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 $A_j\in\mathbb{B}(\mathcal{H})$, $0\le A_j < I_\mathcal{H}$, $A_j's$ are trace class operators and $A_1 \le A_j \le A_n~(j=1,\cdots,n)$ and $\sum_{j=1}^n\lambda_j=1,~ \lambda_j \ge 0~ (j=1,\cdots,n)$. In addition, we present some new versions of the Lewent type determinantal inequality.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
632
638
http://www.aot-math.org/article_58027_e4993959d2838f85d7a990cb957c644c.pdf
dx.doi.org/10.15352/aot.1711-1259
wUR modulus and normal structure in Banach spaces
Ji
Gao
author
text
article
2018
eng
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 $f\in S(X^*),$ then $X$ has weak normal structure.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
639
646
http://www.aot-math.org/article_58068_bab5247b1aec6e648c85b7d2223d9400.pdf
dx.doi.org/10.15352/aot.1801-1295
The matrix power means and interpolations
DINH
Trung Hoa
author
Raluca
Dumitru
author
Jose A.
Franco
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
647
654
http://www.aot-math.org/article_58111_2db06770ff58292e14a48df88a3e8429.pdf
dx.doi.org/10.15352/aot.1801-1288
$C^*$-algebra distance filters
Tristan
Bice
author
Alessandro
Vignati
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
655
681
http://www.aot-math.org/article_58258_60253d2648889c6465fbb303065fad63.pdf
dx.doi.org/10.15352/aot.1710-1241
On Neugebauer's covering theorem
Jésus M.
Aldaz
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
682
689
http://www.aot-math.org/article_58259_27f6aa7b3ddc36299f175589a7784c20.pdf
dx.doi.org/10.15352/aot.1711-1262
The existence of hyper-invariant subspaces for weighted shift operators
Hossein
Sadeghi
University of Zanjan
author
Farzollah
Mirzapour
University of Zanjan
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
690
698
http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdf
dx.doi.org/10.15352/aot.1802-1316
Orthogonality of bounded linear operators on complex Banach spaces
Kallol
Paul
Department of Mathematics
Jadavpur University
Kolkata 700032
India
author
Debmalya
Sain
Indian Institute of Science, Bengaluru
author
Arpita
Mal
Department of Mathematics
Jadavpur University
Kolkata 700032
India
author
Kalidas
Mandal
Department of Mathematics
Jadavpur University
Kolkata 700032
India
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
699
709
http://www.aot-math.org/article_58482_7dbaeeafc2780dac3d0996c2d9a48612.pdf
dx.doi.org/10.15352/aot.1712-1268
Affine actions and the Yang-Baxter equation
Dilian
Yang
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
710
730
http://www.aot-math.org/article_60104_5b1e93d062f80db45bd3e9f530226155.pdf
dx.doi.org/10.15352/aot.1801-1298
Characterizing projections among positive operators in the unit sphere
Antonio
Peralta
Universidad de Granada
author
text
article
2018
eng
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 $$Sph(E;P) :=\left\{ x\in P : \|x-b\|=1 \hbox{ for all } b\in E \right\}.$$ Given a $C^*$-algebra $A$ and a subset $E\subset A,$ 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 $$Sph^+_{K(H_2)} \left( Sph^+_{K(H_2)}(a) \right) =\left\{ b\in S(K(H_2)^+) : \!\! \begin{array}{c}s_{_{K(H_2)}} (a) \leq s_{_{K(H_2)}} (b), \hbox{ and }\\ \textbf{1}-r_{_{B(H_2)}}(a)\leq \textbf{1}-r_{_{B(H_2)}}(b) \end{array}\right\},$$ 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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
3
no.
2018
731
744
http://www.aot-math.org/article_60341_1b13a753583eb613f2eecd19bf0bb7e9.pdf
dx.doi.org/10.15352/aot.1804-1343