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Uniform Smoothness and Property (I)


Affiliations
1 Cleveland State University, Department of Mathematics, Cleveland, Ohio 44115, United States
     

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An interesting theorem due to Phelps implies that a Banach space is smooth if and only if every finite dimensional subspace has Mazur Intersection Property, also know as property (I). The purpose of this note is to obtain a similar characterization of uniformly smooth Banach spaces in terms of the property (I).

Keywords

Property (I), Uniform Smoothness, Ultrapower.
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  • Uniform Smoothness and Property (I)

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Authors

K. Sundaresan
Cleveland State University, Department of Mathematics, Cleveland, Ohio 44115, United States

Abstract


An interesting theorem due to Phelps implies that a Banach space is smooth if and only if every finite dimensional subspace has Mazur Intersection Property, also know as property (I). The purpose of this note is to obtain a similar characterization of uniformly smooth Banach spaces in terms of the property (I).

Keywords


Property (I), Uniform Smoothness, Ultrapower.