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Auerbach's theorem and tensor products of Banach spaces

Published online by Cambridge University Press:  24 October 2008

A. F. Ruston
A. F. Ruston
Affiliation:
Department of Pure MathematicsUniversity of Sheffield
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Extract

In his well-known treatise, Banach mentions that there exist complete normed bi-orthogonal systems in any finite-dimensional (real) Banach space—a result he attributes to H. Auerbach ((1), p. 238). The purpose of this note is to present a proof of this result (valid for complex as well as real Banach spaces), and to give some applications to the theory of tensor products of Banach spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 3 , July 1962 , pp. 476 - 480
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

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