Related papers: Generalized Drazin invertibility of operator matri…

Drazin inverses are a special kind of generalized inverses that can be defined for endomorphisms in any category. A natural question to ask is whether one can somehow extend the notion of Drazin inverse to arbitrary maps - not simply…

Let $X$ a Banach space and $T$ a bounded linear operator on $X.$ We denote by $S(T)$ the set of all $\lambda \in \cit$ such that $T$ does not have the single-valued extension property at $\lambda$. In this note we prove equality up to…

Given a complex Banach space $X$, let $\mathcal{B}(X)$ be the collection of all bounded linear operators on $X.$ For $A,B\in\mathcal{B}(X)$ we define $A,B$ are $A$-weakly commutative if there exists $C\in\mathcal{B}(X)$ satisfying…

Let $\mathcal{A}$ be a complex Banach algebra. An element $a\in \mathcal{A}$ has g-Drazin inverse if there exists $b\in \mathcal{A}$ such that $$b=bab, ab=ba, a-a^2b\in \mathcal{A}^{qnil}.$$ Let $a,b\in \mathcal{A}$ have g-Drazin inverses.…

A linear operator $U$ acting boundedly on an infinite-dimensional separable complex Hilbert space $H$ is universal if every linear bounded operator acting on $H$ is similar to a scalar multiple of a restriction of $U$ to one of its…

A Hilbert space operator $A\in\B$ is left $(X,m)$-invertible by $B\in\B$ (resp., $B\in\B$ is an $(X,m)$-adjoint of $A\in\B$) for some operator $X\in\B$ if…

The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the…

A Hilbert space operator $T\in B$ is $(m,P)$-expansive, for some positive integer $m$ and operator $P\in B$, if $\sum_{j=0}^m{(-1)^j\left(\begin{array}{clcr}m\\j\end{array}\right)T^{*j}PT^j}\leq 0$. No Drazin invertible operator $T$ can be…

A real square matrix $A$ is called a P-matrix if all its principal minors are positive. Using the sign non-reversal property of matrices, the notion of P-matrix has been recently extended by Kannan and Sivakumar to infinite-dimensional…

A generalized inversion of block T+H matrix is obtained for the first time. In a particular case when T+H matrix is invertible, the method allows to obtain its inverse matrix without an additional condition of invertibility of the…

In this paper the properties of right invertible row operators, i.e., of 1X2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the…

We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of $n\times n$ operator matrices by using non-negative…

We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inverses of $2\times 2$ block operator matrices. These…

In this paper we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the…

We introduce unbounded multipliers on operator spaces. These multipliers generalize both, regular operators on Hilbert C*-modules and (bounded) multipliers on operator spaces.

There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…

Let $T_n^d(A)$ denote a partial upper triangular operator matrix whose diagonal entries are given and the others unknown. In this article we have aim to find characterizations of (left,right) invertibility of $T_n^d(A)$ in terms of diagonal…

The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…

In this paper, we investigate the invertibility of $I_Y+\delta TT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in…

In this paper, we give a new characterization of generalized Browder's theorem by considering equality between the generalized Drazin-meromorphic Weyl spectrum and the generalized Drazin-meromorphic spectrum. Also, we generalize Cline's…