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....
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Compactness and weak compactness of gradient maps
Compactness conditions for elementary operators
Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.
Compactness criteria in function spaces
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency than the classical conditions. The result is first stated and proved for , and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.
Compactness in approximation spaces
In this paper we give a characterization of the relatively compact subsets of the so-called approximation spaces. We treat some applications: (1) we obtain some convergence results in such spaces, and (2) we establish a condition for relative compactness of a set lying in a Besov space.
Compactness in certain abstract function spaces with application to differential inclusions
In this note we present a result on compactness in certain Banach spaces of vector valued functions. We demonstrate an application of this result to the questions of existence of solutions of nonlinear differential inclusions on a Banach space.
Compactness in L¹ of a vector measure
We study compactness and related topological properties in the space L¹(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norming subset of the dual unit ball of L¹(m) appears in our discussion and we study when it is a boundary. The (almost) complete continuity of the integration...