Related papers: Non-Asplund Banach spaces and 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…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of…

First we give a counterexample showing that recent results on separate order continuity of Arens extensions of multilinear operators cannot be improved to get separate order continuity on the product of the whole of the biduals. Then we…

We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with…

This paper deals with the extension of a classical theorem by R. Phelps on the G\^ateaux differentiability of Lipschitz functions on separable Banach spaces to the non-separable case. The extension of the theorem is not possible for general…

Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a (bounded or unbounded) scalar type spectral operator $A$ in a complex Banach space as well as of the…

We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on Banach spaces of sequences on Z and the spectrum of operators commuting with the shift on Banach spaces of sequences on Z^+.We generalize the…

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 show that if $T$ is an isometry (as metric spaces) from an open subgroup of the invertible group $A^{-1}$ of a unital Banach algebra $A$ onto an open subgroup of the invertible group $B^{-1}$ of a unital Banach algebra $B$, then $T$ is…

In this paper, considering a real Banach sequence lattice Y instead of a Lebesgue sequence space $l_p$ we generalize p-convexity of a linear operator $T:E\to X$, where E is a Banach space and X is a Banach lattice. Then we prove that basic…

We extend the Paley-Wiener pertubation theory to linear operators mapping a subspace of one Banach space into another Banach space.

The goal of this paper is to study band-dominated operators on Banach spaces with Schauder basis with respect to uniformly locally finite metric spaces as well as the Banach algebras generated by them: the so called uniform Roe algebras. We…

Let $\mathbb{X}$ be a Banach space and let $\mathbb{X}^*$ be the dual space of $\mathbb{X}.$ For $x,y \in \mathbb{X},$ $ x$ is said to be $T$-orthogonal to $y$ if $Tx(y) =0,$ where $T$ is a bounded linear operator from $\mathbb{X}$ to…

We prove that reiteratively hypercyclic operators have perfect spectrum. Consequently, it follows that there exist separable infinite dimensional Banach spaces that do not support any reiteratively hypercyclic operator. For this, we study…

The main result: the dual of separable Banach space $X$ contains a total subspace which is not norming over any infinite dimensional subspace of $X$ if and only if $X$ has a nonquasireflexive quotient space with the strictly singular…

We give a characterization of the operators on the injective tensor product $E \hat{\otimes}_\varepsilon X$ for any separable Banach space $E$ and any (non-separable) Banach space $X$ with few operators, in the sense that any operator $T: X…

We characterize those classes $\ccc$ of separable Banach spaces admitting a separable universal space $Y$ (that is, a space $Y$ containing, up to isomorphism, all members of $\ccc$) which is not universal for all separable Banach spaces.…

In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish the close connection between the classical Bohr radius and the arithmetic Bohr radius of bounded…

Let $\{\tau_j\}_{j=1}^n$ be a collection in a finite dimensional Banach space $\mathcal{X}$ of dimension $d$ and $\{f_j\}_{j=1}^n$ be a collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) such that $f_j(\tau_j) =1$, $\forall 1\leq j\leq…