Compact operators and approximation spaces
We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.
Compact operators between K- and J-spaces
The paper establishes necessary and sufficient conditions for compactness of operators acting between general K-spaces, general J-spaces and operators acting from a J-space into a K-space. Applications to interpolation of compact operators are also given.
Compact Operators in Type III... and Type III... Factors.
Compact operators on Orlicz spaces
Compact operators whose adjoints factor through subspaces of
For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if , where p’ = p/(p-1) and . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of in a particular manner. The normed operator ideals of p-compact operators and of weakly p-compact operators, arising from these factorizations,...
Compact polynomials between Banach spaces.
Compact sets in
Compact sets of tight measures
Compact spaces that do not map onto finite products
We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
Compact Subsets of Partially Ordered Banach Spaces.
Compact subsets of spaces of holomorphic functions.
Compact weighted composition operators on spaces of continous functions: A survey.
Compactification and compactoidification
Compactly Determined Locally Convex Topologies.
Compactly epi-Lipschitzian convex sets and functions in normed spaces.
Compactly supported distributions and unitary representations. (Distributions à support compact et représentations unitaires.)
Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators
A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with...
Compactly Supported Refinable Distributions in Triebel-Lizorkin Spaces and Besov Spaces.
Compactness and countable compactness in weak topologies
A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact....