Related papers: Generalized Drazin invertibility of operator matri…
We will give an outline of the main results in our recent AMS Memoir, and include some new results, exposition and open problems. In that memoir we developed a general dilation theory for operator valued measures acting on Banach spaces…
We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
Consider a complex unital Banach algebra $\mathcal{A}.$ For $x_1,x_2,x_3\in\mathcal{A},$ in this paper, we establish that under certain assumptions on $x_1,x_2,x_3$, Drazin (resp. g-Drazin) invertibility of any three elements among…
In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of $v$, namely $v\in \mathbb{R}$. These modified inequalities are used to establish corresponding operator inequalities on a…
Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (\alpha_j -A)^{-1}$ are given. Several examples are considered.
We show that several known facts concerning roots of matrices generalize to operator algebras and Banach algebras. We show for example that the so-called Newton, binomial, Visser, and Halley iterative methods converge to the root in Banach…
This paper studies the issues about the generalized inverses of tensors under the C-Product. The aim of this paper is threefold. Firstly, this paper present the definition of the Moore-Penrose inverse, Drazin inverse of tensors under the…
We present new generalized Jacobson's lemma for generalized Drazin inverses. This extend the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear $\&$ Multilinear Algebra, {\bf 68}(2020), 81--93).
We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces
In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal…
In this note, a general version of Bessel multipliers in Hilbert $C^*$-modules is presented and then, many results obtained for multipliers are extended. Also the conditions for invertibility of generalized multipliers are investigated in…
Let $R$ be an associative ring with unit $1$, and $a, b, c\in R$ satisfy $a(ba)^{2}=abaca=acaba=(ac)^{2}a$, this paper proves that $1-ac$ has generalized Drazin inverse (Drazin inverse, pseudo Drazin inverse, respectively) if and only if…
In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that…
We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of the category theory. The notion of minors is generalised…
We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
In this paper, we establish the invertibility of the Berezin transform of the symbol as a necessary and sufficient condition for the invertibility of the Toeplitz operator on the Bergman space $L^2_a(\mathbb{D})$. More precisely, if ${\phi}…
The notion of decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator, in sense that a mapping is replaced by a binary relation.…