@Article{Mohammadhasani2018,
author="Mohammadhasani, Ahmad
and Ilkhanizadeh Manesh, Asma",
title="Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="451-458",
abstract="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].",
issn="2538-225X",
doi="10.15352/aot.1709-1225",
url="http://www.aot-math.org/article_53654.html"
}
@Article{Alomari2018,
author="Alomari, Mohammad",
title="Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="459-472",
abstract="In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .",
issn="2538-225X",
doi="10.15352/aot.1708-1220",
url="http://www.aot-math.org/article_54087.html"
}
@Article{Ganesh2018,
author="Ganesh, Jadav
and Ramesh, Golla
and Sukumar, Daniel",
title="Perturbation of minimum attaining operators",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="473-490",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1708-1215",
url="http://www.aot-math.org/article_54270.html"
}
@Article{Kostic2018,
author="Kostic, Marko",
title="Besicovitch almost automorphic solutions of nonautonomous differential equations of first order",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="491-506",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1711-1257",
url="http://www.aot-math.org/article_54492.html"
}
@Article{Haralampidou2018,
author="Haralampidou, Marina
and Tzironis, Konstantinos",
title="A Kakutani-Mackey-like theorem",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="507-521",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1712-1270",
url="http://www.aot-math.org/article_56029.html"
}
@Article{Liao2018,
author="Liao, Fanghui
and Liu, Zongguang
and Wang, Hongbin",
title="$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="522-537",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1709-1236",
url="http://www.aot-math.org/article_57072.html"
}
@Article{Das2018,
author="Das, Namita
and Behera, Jitendra",
title="Fixed points of a class of unitary operators",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="538-550",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1710-1244",
url="http://www.aot-math.org/article_57403.html"
}
@Article{Hezzi2018,
author="Hezzi, Hanen",
title="Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with critical exponential growth",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="551-581",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1709-1227",
url="http://www.aot-math.org/article_57444.html"
}
@Article{Roidos2018,
author="Roidos, Nikolaos",
title="Closedness and invertibility for the sum of two closed operators",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="582-605",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1801-1297",
url="http://www.aot-math.org/article_57481.html"
}
@Article{Truong2018,
author="Truong, Tuyen
and Trang, Nguyen",
title="Parallel iterative methods for solving the common null point problem in Banach spaces",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="606-619",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1710-1246",
url="http://www.aot-math.org/article_57735.html"
}
@Article{Chō2018,
author="Chō, Muneo
and Lee, Ji Eun
and Prasad, T.
and Tanahashi, Kôtarô",
title="Complex isosymmetric operators",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="620-631",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1712-1267",
url="http://www.aot-math.org/article_57759.html"
}
@Article{Morassaei2018,
author="Morassaei, Ali",
title="Variant versions of the Lewent type determinantal inequality",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="632-638",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1711-1259",
url="http://www.aot-math.org/article_58027.html"
}
@Article{Gao2018,
author="Gao, Ji",
title="wUR modulus and normal structure in Banach spaces",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="639-646",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1801-1295",
url="http://www.aot-math.org/article_58068.html"
}
@Article{TrungHoa2018,
author="Trung Hoa, DINH
and Dumitru, Raluca
and Franco, Jose A.",
title="The matrix power means and interpolations",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="647-654",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1801-1288",
url="http://www.aot-math.org/article_58111.html"
}
@Article{Bice2018,
author="Bice, Tristan
and Vignati, Alessandro",
title="$C^*$-algebra distance filters",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="655-681",
abstract="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. ",
issn="2538-225X",
doi="10.15352/aot.1710-1241",
url="http://www.aot-math.org/article_58258.html"
}
@Article{Aldaz2018,
author="Aldaz, Jésus M.",
title="On Neugebauer's covering theorem",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="682-689",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1711-1262",
url="http://www.aot-math.org/article_58259.html"
}
@Article{Sadeghi2018,
author="Sadeghi, Hossein
and Mirzapour, Farzollah",
title="The existence of hyper-invariant subspaces for weighted shift operators",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="690-698",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1802-1316",
url="http://www.aot-math.org/article_58113.html"
}
@Article{Paul2018,
author="Paul, Kallol
and Sain, Debmalya
and Mal, Arpita
and Mandal, Kalidas",
title="Orthogonality of bounded linear operators on complex Banach spaces",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="699-709",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1712-1268",
url="http://www.aot-math.org/article_58482.html"
}
@Article{Yang2018,
author="Yang, Dilian",
title="Affine actions and the Yang-Baxter equation",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="710-730",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1801-1298",
url="http://www.aot-math.org/article_60104.html"
}
@Article{Peralta2018,
author="Peralta, Antonio",
title="Characterizing projections among positive operators in the unit sphere",
journal="Advances in Operator Theory",
year="2018",
volume="3",
number="3",
pages="731-744",
abstract="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.",
issn="2538-225X",
doi="10.15352/aot.1804-1343",
url="http://www.aot-math.org/article_60341.html"
}