Related papers: Constructing Well-bounded Operators not of type (B…

We investigate the space of bounded linear operators on a Banach space equipped with a norm which is equivalent to the operator norm such that the subspace of compact operators is an M-ideal. In particular, we observe that the space of…

Parallel to the study of finite dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces H_n^k,0< k < n+1, generalizing the row and column…

In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…

We address the following two questions regarding the maximal left ideals of the Banach algebra $\mathscr{B}(E)$ of bounded operators acting on an infinite-dimensional Banach pace $E$: (Q1) Does $\mathscr{B}(E)$ always contain a maximal left…

We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We…

In this paper, we study the boundedness and the compactness of the little Hankel operators $h_b$ with operator-valued symbols $b$ between different weighted vector-valued Bergman spaces on the open unit ball $\mathbb{B}_n$ in…

In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly…

Let $V\subseteq W$ be two operator spaces. Arveson-Wittstock-Hahn-Banach theorem asserts that every completely contractive map $\varphi:V\to \mathcal{B}(H)$ has a completely contractive extension $\tilde{\varphi}:W\to \mathcal{B}(H)$, where…

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the…

We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…

We study automatic injectivity of surjective algebra homomorphisms from $\mathscr{B}(X)$, the algebra of (bounded, linear) operators on $X$, to $\mathscr{B}(Y)$, where $X$ is one of the following \emph{long} sequence spaces: $c_0(\lambda)$,…

We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?

We consider a bounded linear operator $T$ on a complex Banach space $X$ and show that its spectral radius $r(T)$ satisfies $r(T) < 1$ if all sequences $(< x',T^nx>)_{n \in \mathbb{N}_0}$ ($x \in X$, $x' \in X'$) are, up to a certain…

A bounded operator $u$ on $X$ is called rigid when there is an increasing sequence of positive integers $(n_k)_{k\geq 1}$, such that for every $x$ in $X$ we have $\lim_{k \rightarrow +\infty} u^{n_k} x = x$. For any $r$ in $[0,1]$, we…

We prove that the index formula for $b$-elliptic cone differential operators given by M. Lesch holds verbatim for operators whose coefficients are not necessarily independent of the normal variable near the boundary. We also show that, for…

In this paper we prove that a positive commutator between a positive compact operator $A$ and a positive operator $B$ is in the radical of the Banach algebra generated by $A$ and $B$. Furthermore, on every at least three-dimensional Banach…

The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also…

We look for an effective description of the algebra D_{Lie}(X,B) of operators on a bimodule X over an algebra B, generated by inner derivations. It is shown that in some important examples D_{Lie}(X,B) consists of all elementary operators…

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…

It is proved that a commutative algebra $A$ of operators in a reflexive real Banach space has an invariant subspace if each operator $T\in A$ satisfies the condition $$\|1- \varepsilon T^2\|_e \le 1 + o(\varepsilon) \text{ when }…