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A Banach Space in Which a Ball is Contained in the Range of Some Countably Additive Measure is Superreflexive

Published online by Cambridge University Press:  20 November 2018

Yeneng Sun
Yeneng Sun*
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801 USA
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Abstract

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A nonstandard proof of the fact that a Banach space in which a ball is contained in the range of a countably additive measure is superreflexive is given. The proof is an application of a general method in which we first transfer certain standard objects to the nonstandard hull of a Banach space and then, using the quite well developed theory of nonstandard hulls, derive results about the objects in the original Banach space. It also provides us with an example of the applications of the theory of nonstandard hull valued measures.

Keywords

28E0546G1003H0546B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 45 - 49
Copyright
Copyright © Canadian Mathematical Society 1990

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