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Proximal Analysis and Boundaries of Closed Sets in Banach Space. Part II: Applications

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein  and
H. M. Strojwas
J. M. Borwein
Affiliation:
Dalhousie University, Halifax, Nova Scotia
H. M. Strojwas
Affiliation:
Carnegie-Mellon University, Pittsburgh, Pennsylvania
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This paper is a direct continuation of the article “Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory”, by the same authors. It is devoted to a detailed analysis of applications of the theory presented in the first part and of its limitations.

Theorem 2.1 has important consequences for geometry of Banach spaces. We start the presentation with a discussion of density and existence of R-proper points (Definition 1.3) for closed sets in Banach spaces. Our considerations will be based on the “lim inf” inclusions proven in the first part of our paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 2 , 01 April 1987 , pp. 428 - 472
Copyright
Copyright © Canadian Mathematical Society 1987

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