Related papers: On generalized core-EP invertibility in a Banach a…
The notion of the core inverse of tensors with the Einstein product was introduced, very recently. This paper we establish some sufficient and necessary conditions for reverse-order law of this inverse. Further, we present new results…
Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given.
We investigate properties of the group inverse in rings with unit related to products and differences of idempotents, and thus we extend some results from \cite{DENG} to more general settings. We show that most part of \cite{DENG} is easily…
The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…
In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank…
We introduce and study a new class of generalized inverse in rings. An element $a$ in a ring $R$ has generalized Hirano inverse if there exists some $b\in R$ such that $bab=b, b\in comm^2(a), a^2-ab \in R^{qnil}$
We give a systematic construction of inverse-closed (Banach) subalgebras in general higher-dimensional non-commutative tori
The purpose of this paper is to characterize several classes of functional identities involving inverses with related mappings from a unital Banach algebra $\mathcal{A}$ over the complex field into a unital $\mathcal{A}$-bimodule…
We generalize results of Davie and Raeburn describing homotopy types of the group of invertible elements and of the set of idempotents of the projective tensor product of complex unital Banach algebras. We illustrate our results by specific…
It is well known that a square complex matrix is called EP if it commutes with its Moore-Penrose inverse. In this paper, new classes of matrices which extend this concept are characterized. For that, we consider commutative equalities given…
We investigate the Hirano invertibility of block-operator matrices in Banach algebras, and obtain the Hirano inverse of matrix $\begin{bmatrix} A&B\\ C&D \end{bmatrix}$ under two types of new perturbation conditions. Furthermore, we provide…
Given a (not necessarily continuous) homomorphism between Banach algebras $\T\colon\A\to\B$, an element $a\in\A$ will be said to be B-Fredholm (respectively generalized B-Fredholm) relative to $\T$, if $\T(a)\in \B$ is Drazin invertible…
Let $S$ be a $*$-semigroup and let $a,w,v\in S$. The initial goal of this work is to introduce two new classes of generalized inverses, called the $w$-core inverse and the dual $v$-core inverse in $S$. An element $a\in S$ is $w$-core…
In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed…
We present some basic elements of the theory of generalised Br\`{e}gman relative entropies over nonreflexive Banach spaces. Using nonlinear embeddings of Banach spaces together with the Euler--Legendre functions, this approach unifies two…
Let $G$ be a discrete group, let $p\ge1$, and let $\omega$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $\omega$ for $\ell^p(G,\omega)$ to be a Banach algebra admitting a norm-controlled…
This paper studies the concept of stable perturbation $B\in\mathbb{C}^{n\times n}$ for the core-EP inverse of a matrix $A\in\mathbb{C}^{n\times n}$ with index $k$. For a given stable perturbation $B$ of $A$, explicit expressions of its…
Let $R$ be an associative ring with an identity and suppose that $a,b,c,d \in R$ satisfy $bdb = bac,dbd = acd$. If $ac$ has generalized Drazin ( respectively, pseudo Drazin, Drazin) inverse, we prove that $bd$ has generalized Drazin…
Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…
We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call,…