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Rotundity redux

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

A. C. Yorke
A. C. Yorke
Affiliation:
School of Mathematical and Physical Sciences Murdoch UniversityMurdoch, W. A. 6150, Australia
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Abstract

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Recently the concept of uniform rotundity was generalized for real Banach spaces by using a type of “area” devised for these spaces. This paper modifies the methods used for uniform rotundity and applies them to weak rotundity in real and complex spaces. This leads to the definition of k-smoothness, k-very smoothness and k-strong smoothness. As an application, several sufficient conditions for reflexivity are obtained.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 143 - 151
Copyright
Copyright © Australian Mathematical Society 1985

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