Related papers: On simultaneous similarity of families of commutin…
Cotype is used in this paper to prove new results concerning the existence of non-absolutely summing linear operators between Banach spaces. We derive consequences that extend/generalize/ complement some classic results. We also point out…
In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem.
A closed subspace of a Banach space $\cX$ is almost-invariant for a collection $\cS$ of bounded linear operators on $\cX$ if for each $T \in \cS$ there exists a finite-dimensional subspace $\cF_T$ of $\cX$ such that $T \cY \subseteq \cY +…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…
We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in…
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…
We consider similarity transformations of a perturbed linear operator $A-B$ in a complex Banach space $\mathcal{X}$, where the unperturbed operator $A$ is a generator of a Banach $L_1(\mathbb{R})$-module and the perturbation operator $B$ is…
First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on $L^1+L^\infty$ with…
We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…
This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…
In this article, we develop a framework for the joint functional calculus of commuting pair of $\text{Ritt}_{\text{E}}$ operators on Banach spaces. We establish a transfer principle that relates the bounded holomorphic functional calculus…
We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…
In this paper we prove coincidence results concerning spaces of absolutely summing multilinear mappings between Banach spaces. The nature of these results arises from two distinct approaches: the coincidence of two \textit{a priori}…
This paper concerns the enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field. This is the same as the classification of commuting tuples of matrices over a finite field up to…
In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is…
In this paper, a new criterion for the similarity of commuting tuples of operators on Hilbert spaces is introduced. As an application, we obtain a geometric similarity invariant of tuples in the Cowen-Douglas class which gives a partial…
The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1976]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map I_X…
In this work I investigate uniformly continuous semigroups of sublinear transition operators on the Banach space of bounded real-valued functions on some countable set. I show how the family of exponentials of a bounded sublinear rate…
In this paper, we explore the concept of multilinear operators that are multiple almost summing and present a new concept of type and cotype of multilinear operators and investigate the conditions for this new concept to recover the…