Related papers: Compact-Like Operators in Lattice-Normed Spaces
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of…
We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…
Let $E$ be a sublattice of a vector lattice $F$. A net $\{ x_\alpha \}_{\alpha \in \mathcal{A}}\subseteq E$ is said to be $ F $-order convergent to a vector $ x \in E$ (in symbols $ x_\alpha \xrightarrow{Fo} x $ in $E$), whenever there…
We study the representation of non-weakly compact operators between $AL$-spaces. In this setting, we show that every operator admits a best approximant in the ideal of weakly compact operators. Using duality arguments, we extend this result…
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and…
Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not…
We introduce the class of operator $p$-compact mappings and completely right $p$-nuclear operators, which are natural extensions to the operator space framework of their corresponding Banach operator ideals. We relate these two classes,…
We show that a compact operator $A$ is a multiple of a positive semi-definite operator if and only if $$ \sigma(AB) \subseteq \overline{W(A)W(B)}, \quad\text{for all (rank one) operators $B$}. $$ An example of a normal operator is given to…
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…
A pair of functions defined on a set X with values in a vector space E is said to be disjoint if at least one of the functions takes the value 0 at every point in X. An operator acting between vector-valued function spaces is disjointness…
We consider this and related questions: When is a finite linear combination of composition operators, acting on the Hardy space or the standard weighted Bergman spaces on the unit disk, a compact operator?
We study when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can…
We study almost L(M) weakly compact and order L(M) weakly compact operators in Banach spaces. Several further topics related to these operators are investigated.
In this paper, using the concept of unbounded absolute weak convergence ($uaw$-convergence, for short) in a Banach lattice, we define two classes of continuous operators, named $uaw$-Dunford-Pettis and $uaw$-compact operators. We…
We investigate the $o\tau$-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the KB operators between locally solid lattices and topological vector spaces; and the Levi operators from…
Let $X$ be a rearrangement-invariant space. An operator $T: X\to X$ is called narrow if for each measurable set $A$ and each $\epsilon > 0$ there exists $x \in X$ with $x^2= \chi_A, \int x d \mu = 0$ and $\| Tx \| < \epsilon$. In particular…
The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact…
In this paper, almost Dunford-Pettis operators with ranges in $c_0$ are used to identify totally bounded sets in the absolute weak topology. That is, a bounded subset $A$ of a Banach lattice $E$ is $|\sigma|(E,E^\prime)$-totally bounded if…
In this paper, the definition of noncommutative Orlicz sequence spaces is given, these spaces generalize the Schatten classes Sp(H). After some relations of trace and norm on this spaces have been researched, one give the criterion of…
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…