A Characterization of Norm Compactness in the Bochner Space $L^p (G ; B)$ For an Arbitrary Locally Compact Group $G$

Josh Isralowitz

A Characterization of Norm Compactness in the Bochner Space $L^p (G ; B)$ For an Arbitrary Locally Compact Group $G$

Functional Analysis 2007-05-23 v3 Classical Analysis and ODEs

Authors: Josh Isralowitz

Abstract

In this paper, we generalize a result of N. Dinculeanu which characterizes norm compactness in the Bochner space $L^p(G ; B)$ in terms of an approximate identity and translation operators, where $G$ is a locally compact abelian group and $B$ is a Banach space. Our characterization includes the case where $G$ is nonabelian, and we weaken the hypotheses on the approximate identity used, providing new results even for the case $B = \mathbb{C}$ and $G = \mathbb{R}^n.$

Keywords

bochner space norm compactness locally compact group approximate identity translation operators banach space

Cite

@article{arxiv.math/0401333,
  title  = {A Characterization of Norm Compactness in the Bochner Space $L^p (G ; B)$ For an Arbitrary Locally Compact Group $G$},
  author = {Josh Isralowitz},
  journal= {arXiv preprint arXiv:math/0401333},
  year   = {2007}
}

Comments

13 pages, accepted into the "Journal of Mathematical Analysis and Applications."

A Characterization of Norm Compactness in the Bochner Space $L^p (G ; B)$ For an Arbitrary Locally Compact Group $G$

Abstract

Keywords

Cite

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