Kulkarni, S. H. Ramesh, G.
Published in
Indian Journal of Pure and Applied Mathematics

Let H1, H2 be complex Hilbert spaces and T be a densely defined closed linear operator from its domain D(T), a dense subspace of H1, into H2. Let N(T) denote the null space of T and R(T) denote the range of T. Recall that C(T):= D(T) ∩ N(T)⊥ is called the carrier space of T and the reduced minimum modulus γ(T) of T is defined as: γ(T):=inf{‖T(x)‖:x...

Fatehi, Mahsa Hammond, Christopher N. B.
Published in
Complex Analysis and Operator Theory

We investigate the properties of weighted composition–differentiation operators acting on the Hardy space H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{2}$$\end{...

Ahmad, Naeem
Published in
Advances in Operator Theory

In this paper, we introduce a new family of operators which is called polynomially-m-B-normal (resp-quasi polynomially B-normal). Some of the basic properties of members of these families are studied.

Roman, Marcel Sandovici, Adrian
Published in
Complex Analysis and Operator Theory

The main goal of this paper is to provide a complete description of the operator solutions (eventually multivalued) of the (multivalued) operator equation A∗A=λAn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength...

Waziri, Mohammed Yusuf Yusuf, Aliyu Abubakar, Auwal Bala
Published in
Computational and Applied Mathematics

In this paper, we propose a hybrid conjugate gradient (CG) method based on the approach of convex combination of Fletcher–Reeves (FR) and Polak–Ribière–Polyak (PRP) parameters, and Quasi-Newton’s update. This is made possible by using self-scaling memory-less Broyden’s update together with a hybrid direction consisting of two CG parameters. However...

Sertbaş, Meltem Saral, Coşkun
Published in
Complex Analysis and Operator Theory

In this study the minimal and maximal operator generated by q-difference expression and their adjoint operators are introduced in Lq2(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} ...

Duggal, Bhagwati Prashad Kim, In Hyun
Published in
Demonstratio Mathematica

Given Hilbert space operators T , S ∈ B ( ℋ ) T,S\in B( {\mathcal H} ) , let Δ \text{Δ} and δ ∈ B ( B ( ℋ ) ) \delta \in B(B( {\mathcal H} )) denote the elementary operators Δ T , S ( X ) = ( L T R S − I ) ( X ) = T X S − X {\text{Δ}}_{T,S}(X)=({L}_{T}{R}_{S}-I)(X)=TXS-X and δ T , S ( X ) = ( L T − R S ) ( X ) = T X − X S {\delta }_{T,S}(X)=({L}_{T...

Bensaid, Ikram Fatima Zohra Dehimi, Souheyb Fuglede, Bent Mortad, Mohammed Hichem
Published in
Advances in Operator Theory

In this paper, we show new versions of the Fuglede theorem in an unbounded setting. A related counterexample is also presented. In the second part of the paper, we give a pair of a closed and a self-adjoint (unbounded) operator which is not intertwined by any (bounded or closed) operator except the zero operator.

Feki, Kais
Published in
Advances in Operator Theory

This paper is concerned with linear operators on a complex Hilbert space H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}$$\end{document}, which are bounde...

Han, Deguang Hu, Qianfeng Liu, Rui
Published in
Banach Journal of Mathematical Analysis

A quantum injective frame is a frame that can be used to distinguish density operators (states) from their frame measurements, and the frame quantum detection problem asks to characterize all such frames. This problem was recently settled in Botelho-Andrade et al. (Springer Proc Math Stat 255:337–352, 2017) and Botelho-Andrade et al. (J Fourier Ana...