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Complex convexity and the geometry of Banach spaces

Published online by Cambridge University Press:  24 October 2008

S. J. Dilworth
S. J. Dilworth
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A.
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Extract

The notion of PL-convexity was introduced in [4]. In the present article several results are proved which related PL-convexity to various aspects of the geometry of Banach spaces. The first section introduces the moduli of comples convexity and makes a comparison with the more familiar modulus of uniform convexity. It is shown that unconditional convergence of implies convergence of . In the next section the moduli and are shown to be related. The method of proof gives rise to a theorem about strict c-convexity of Lp(X) and a result on the representability in Lp(X).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 495 - 506
Copyright
Copyright © Cambridge Philosophical Society 1986

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