Related papers: Representation of sequence classes by operator ide…

We study the complementation (in $\ell_\infty$) of the Banach space $c_{0,\mathcal{I}}$, consisting of all bounded sequences $(x_n)$ that $\mathcal{I}$-converge to $0$, endowed with the supremum norm, where $\mathcal{I}$ is an ideal of…

We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$, when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$. In particular, we derive…

A Banach space E is said to have Property (w) if every (bounded linear) operator from E into E' is weakly compact. We give some interesting examples of James type Banach spaces with Property (w). We also consider the passing of Property (w)…

We analyze the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated K\"othe sequence spaces. We establish relationships with spaces of multipliers and apply these results…

In view of the fact that some classical methods to construct multi-ideals fail in constructing hyper-ideals, in this paper we develop two new methods to construct hyper-ideals of multilinear operators between Banach spaces. These methods…

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach algebraic point of view. Namely, we mainly…

In the short note we prove that for every $0<p<1$, there exists an infinite dimensional closed linear subspace of $\mathcal{L}\left( \ell_{p};\ell_{p}\right) $ every nonzero element of which is non $(r,s)$-absolutely summing operator for…

In the framework of operator theory, we investigate a close Lie theoretic relationship between all operator ideals and certain classical groups of invertible operators that can be described as the solution sets of certain algebraic…

We introduce and develop the notion of hyper-ideals of multilinear operators between Banach spaces. While the well studied notion of ideals of multilinear operators (multi-ideals) relies on the composition with linear operators, the notion…

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…

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 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…

V. D. Milman proved in \cite{Milman:70} that the product of two strictly singular operators on $L_p[0,1]$ ($1\le p<\infty$) or on $C[0,1]$ is compact. In this note we utilize Schreier families $\S_\xi$ in order to define the class of…

This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on a Free Banach spaces of countable type. The main goal of this work wil be to formulate a representation theorem for these…

Every composition of two strictly singular operators is compact on the Baernstein space $B_p$ for $1 < p < \infty$ and on the $p$-convexified Schreier space $S_{p}$ for $1 \leq p < \infty$. Furthermore, every subsymmetric basic sequence in…

Let $\mathcal H$ be a complex infinite-dimensional separable Hilbert space, and let $\mathcal K(\mathcal H)$ be the $C^*$-algebra of compact linear operators in $\mathcal H$. Let $(E,\|\cdot\|_E)$ be a symmetric sequence space. If…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.

It is shown that if $1<p<\infty$ and $X$ is a subspace or a quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces, then for any compact operator $T$ on $X$ such that $\|I+T\|>1$, the operator $I+T$ attains its norm. A…

Generalizing classical results of the theory of absolutely summing operators, in this paper we characterize the duals of a quite large class of Banach operator ideals defined or characterized by the transformation of vector-valued…

We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…