Related papers: Weak-star quasi norm attaining operators

This note deals with the question: If T is a linear mapping between Banach spaces X and Y, and x belongs to X and has small norm, is x close to the kernel of T? It draws on notions of Z-stability and provides an affirmative constructive…

A bounded linear operator $T$ on a Banach space $X$ is called hypercyclic if there exists a vector $x \in X$ such that $orb{(x,T)}$ is dense in $X$. The Hypercyclicity Criterion is a well-known sufficient condition for an operator to be…

It is shown that every component of the spectrum of a weakly hypercyclic operator meets the unit circle. The proof is based on the lemma that a sequence of vectors in a Banach space whose norms grow at geometrical rate doesn't have zero in…

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…

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…

We study complex distribution spaces given over a bounded Lipschitz domain $\Omega$ and associated with an elliptic differential operator $A$ with $C^{\infty}$-coefficients on $\overline{\Omega}$. If $X$ and $Y$ are quasi-Banach…

Let $A$ be a bounded linear operator and $P$ a bounded linear projection on a Banach space $X$. We show that the operator semigroup $(e^{t(A-kP)})_{t \ge 0}$ converges to a semigroup on a subspace of $X$ as $k \to \infty$ and we compute the…

The main result of the paper shows that, for 1<p and 1<=q, a linear operator T from l_p to l_q attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p=1).…

In this paper, we introduce a concept of norm-attainment in the projective symmetric tensor product $\widehat{\otimes}_{\pi,s,N} X$ of a Banach space $X$, which turns out to be naturally related to the classical norm-attainment of…

Let $X_1, \ldots, X_m$ be Banach spaces and let $E_1, \ldots, E_m,F$ be Banach lattices. Our main results read as follows: (i) The linear adjoint $A^*$ of a continuous multilinear operator $A \colon X_1 \times \cdots \times X_m \to F$ is…

We investigate M-ideals of compact operators and two distinct properties in norm-attaining operator theory related with M-ideals of compact operators called the weak maximizing property and the compact perturbation property. For Banach…

We prove that if q is in (1,\infty), Y is a Banach space and T is a linear operator defined on the space of finite linear combinations of (1,q)-atoms in R^n which is uniformly bounded on (1,q)-atoms, then T admits a unique continuous…

Let $X$ be a metric space with bounded geometry, $p\in\{0\} \cup [1,\infty]$, and let $E$ be a Banach space. The main result of this paper is that either if $X$ has Yu's Property A and $p\in(1,\infty)$, or without any condition on $X$ when…

Let T be a quasidiagonal operator on a separable Hilbert space. Then T is the norm limit of operators, each of which generate a finite dimensional C*-algebra, if and only if the C*-algebra generated by T is exact.

In this article we extend the notion of quasi-nilpotent equivalent operators, introduced by Colojoara and Foias \cite{co1} for Banach spaces, to the class of bounded operators on sequentially complete locally convex spaces.

Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator $V$ acting on $C[0,1]$ are characterized. From this characterization it follows that $V$ does not determine the topology of…

It is shown that weak quasistability does not imply power boundedness, but coercive power unbounded operators cannot be weakly quasistable.\ Although a finite measure over the unit disc is a Rajchman measure if and only if the position…

If $T$ is a bounded linear operator acting on an infinite-dimensional Banach space $X$, we say that a closed subspace $Y$ of $X$ of both infinite dimension and codimension is an almost-invariant halfspace (AIHS) under $T$ whenever…

Let $X$ be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on $X$ which depend only on the norms of images of elements. This approach is applied to the Daugavet equation…

This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…