Search results for "Locally compact space"

Coderivatives of multivalued mappings, locally compact cones and metric regularity

1999

A note on monolithic scattered compacta

2015

Abstract For a Banach space E, it is well-known that a necessary condition for E to have the controlled separable complementation property (CSCP, for short) is that the dual unit ball B E ⁎ be monolithic in the weak-star topology. We prove here that when X is a scattered first countable locally compact space, then monolithicity of X turns out to be sufficient for C 0 ( X ) to enjoy the CSCP.

Toward a quasi-Möbius characterization of invertible homogeneous metric spaces

2020

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to Mobius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with invertibility. In particular, we provide a new characterization of snowflakes of boundaries of rank-one symmetric spaces of non-compact type among locally compact and connected metric spaces. Furthermore, we investigate the metric implications of homogeneity with respect to uniformly strongly quasi-Mobius self-homeomorphisms, connecting such homogeneity with the combination of uniform bi-Lipschitz homogeneity and quasi-invertibility. In this context we characterize spac…

Locally compact groups which are just not compact

2010

A Just-Non-Compact group, or briefly a JNC group, is a Hausdorff topological group which is not a compact group but all of whose proper Hausdorff quotients are compact groups. Intuitively, it is clear that these groups are rich in compact quotients. Locally compact JNC groups are largely described in the present paper.

Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

2009

Abstract Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.

Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open

2018

We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative weak topology of the unit ball. Stability results of such spaces are established, and we introduce and discuss a geometric condition---property (co)---on a Banach space. Property (co) essentially says that the operation of taking convex combinations of elements of the unit ball is, in a sense, an open map. We show that if a finite dimensional Banach space $X$ has property (co), then for any scattered locally compact Hausdorff space $K$, the space $C_0(K,X)$ of continuous $X$-valued functions vanishing at infinity has…

Polaroid-Type Operators

2018

In this chapter we introduce the classes of polaroid-type operators, i.e., those operators T ∈ L(X) for which the isolated points of the spectrum σ(T) are poles of the resolvent, or the isolated points of the approximate point spectrum σap(T) are left poles of the resolvent. We also consider the class of all hereditarily polaroid operators, i.e., those operators T ∈ L(X) for which all the restrictions to closed invariant subspaces are polaroid. The class of polaroid operators, as well as the class of hereditarily polaroid operators, is very large. We shall see that every generalized scalar operator is hereditarily polaroid, and this implies that many classes of operators acting on Hilbert s…