Related papers: Operators ideals and approximation properties

In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical…

This manuscript presents a systematic study of Calkin algebras -- the quotients $\mathcal{L}(X)/\mathcal{K}(X)$ of bounded operators modulo compact operators on a Banach space $X$ -- and establishes a framework for realizing commutative…

Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such as the Deep Operator…

We explore the norm attainment set and the minimum norm attainment set of a bounded linear operator between Hilbert spaces and Banach spaces. Indeed, we obtain a complete characterization of both the sets, separately for operators between…

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…

We establish a relation between Lipschitz operator ideals and linear operator ideals, which fits in the framework of Galois connection between lattices. We use this relationship to give a criterion which allow us to recognize when a Banach…

We identify the optimal range of the Calder\`{o}n operator and that of the classical Hilbert transform in the class of symmetric quasi-Banach spaces. Further consequences of our approach concern the optimal range of the triangular…

Let $G$ be a locally compact abelian group, let $\nu$ be a regular probability measure on $G$, let $X$ be a Banach space, let $\pi\colon G\to B(X)$ be a bounded strongly continuous representation. Consider the average (or subordinated)…

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

In this article, we give an abstract characterization of the ``identity'' of an operator space $V$ by looking at a quantity $n_{cb}(V,u)$ which is defined in analogue to a well-known quantity in Banach space theory. More precisely, we show…

We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…

We introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the…

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…

We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if $\mathfrak A$ is an ideal of $n$-linear mappings we give conditions for which the following equality $\mathfrak A(E_1,\dots,E_n;F) =…

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…

We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode-Decomposition type…

Averaged operators are important in Convex Analysis and Optimization Algorithms. In this paper, we propose classifications of averaged operators, firmly nonexpansive operators, and proximal operators using the Bauschke-Bendit-Moursi modulus…

A Banach space $X$ has Pe{\l}czy\' nski's property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\to Y$ is weakly compact. In 1962, Aleksander Pe{\l}czy\' nski showed that $C(K)$ spaces for a compact…

We prove when a Banach ideal of linear operators defined, or characterized, by the transformation of vector-valued sequences is maximal. Known results are recovered as particular cases and new information is obtained. To accomplish this…