Related papers: A general abstract approach to approximation prope…
Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in…
We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on…
We use the notion of $\A$-compact sets, which are determined by a Banach operator ideal $\A$, to show that most classic results of certain approximation properties and several Banach operator ideals can be systematically studied under this…
For an operator ideal $\mathcal A$, we study the composition operator ideals ${\mathcal A}\circ{\mathcal K}$, ${\mathcal K}\circ{\mathcal A}$ and ${\mathcal K}\circ{\mathcal A}\circ{\mathcal K}$, where $\mathcal K$ is the ideal of compact…
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…
In this article, we show that the predual $\mathcal{G}_w(U)$ of the weighted space of holomorphic functions has the $\mathcal{I}$- approximation property if and only if $E$ has the $\mathcal{I}$- approximation property, where $\mathcal{I}$…
The powerful concept of an operator ideal on the class of all Banach spaces makes sense in the real and in the complex case. In both settings we may, for example, consider compact, nuclear, or $2$--summing operators, where the definitions…
The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.
We study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded…
The conditions on a Banach space, $E$, under which the algebra, $\mathcal{K}(E)$, of compact operators on $E$ is right flat or homologically unital are investigated. These homological properties are related to factorization in the algebra…
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…
We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are…
In this article, we introduce the Lipschitz bounded approximation property for operator ideals. With this notion, we extend the original work done by Godefroy and Kalton and give some partial answers on the equivalence between the bounded…
We establish new results on the $\mathcal I$-approximation property for the Banach operator ideal $\mathcal I=\mathcal{K}_{up}$ of the unconditionally $p$-compact operators in the case of $1\le p<2$. As a consequence of our results, we…
We study a notion analogous to the $p$-Approximation Property ($p$-AP) for Banach spaces, within the noncommutative context of operator spaces. Referred to as the $p$-Operator Approximation Property ($p$-OAP), this concept is linked to the…
Let (e_i) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a `finite alphabet'. We investigate several…
This paper defines and establishes relations among approximation spaces of certain operators called \textit{H-operators}, which generalize the notion of self-adjoint to Banach spaces.
It has been very recently discovered that there are compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. The aim of this expository paper is to give an overview of those examples and also…
It is well known that weakly $p$-summable sequences in a Banach space $E$ are associated to bounded operators from $\ell_{p^*}$ to $E$, and unconditionally $p$-summable sequences in $E$ are associated to compact operators from $\ell_{p^*}$…
This paper studies the bounded approximation property (BAP) in quasi Banach spaces. In the first part of the paper we show that the kernel of any surjective operator $\ell_p\to X$ has the BAP when $X$ has it and $0<p\leq 1$, which is an…