Related papers: Approximation spaces for H-operators

Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net…

We initiate an investigation into how much the existing theory of (nonselfadjoint) operator algebras on a Hilbert space generalizes to algebras acting on L^p spaces. In particular we investigate the applicability of the theory of real…

For a shift operator $T$ with finite multiplicity acting on a separable infinite dimensional Hilbert space we represent its nearly $T^{-1}$ invariant subspaces in terms of invariant subspaces under the backward shift. Going further, given…

In this article, we give a representation for compact operators acting between reflexive Banach spaces, which generalizes the representation given by Edmunds et al. for compact operators between reflexive Banach spaces with strictly convex…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…

his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem…

For a closed subspace of the range space, we give conditions under which the subspace valued compact operators forms a proximinal subspace of compact operators into the range space.

We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13].

I introduce Banach spaces on which it is possible to precisely characterize the spectrum of the transfer operator associated to a piecewise expanding map with H\"older weight.

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…

In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…

The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator $ A $ on a Hilbert space $ \mathbb{H}, $ we define $ (\epsilon,A)- $approximate…

Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{k\"obaLOC25}, where one is based on the coorbit theory of Feichtinger-Gr\"ochening while the other is…

We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these…

The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…

We review recent work connected with the invariant subspace problem for operators, in particular new developments in the last 15 years. In particular, we include discussions of almost-invariant subspaces, universal operators, specific…

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…

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…

If $p\in [1,+\infty]$ and $T$ is a linear operator with $p$-nuclear adjoint from a Banach space $ X$ to a Banach space $Y$ then if one of the spaces $X^*$ or $Y^{***}$ has the approximation property, then $T$ belongs to the ideal $N^p$ of…