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Transactions of the American Mathematical Society

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Complex convexity in Lebesgue-Bochner Function Spaces


Authors: Patrick N. Dowling, Zhibao Hu and Douglas Mupasiri
Journal: Trans. Amer. Math. Soc. 348 (1996), 127-139
MSC (1991): Primary 28A05, 46E40
DOI: https://doi.org/10.1090/S0002-9947-96-01508-5
MathSciNet review: 1327255
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Abstract: Complex geometric properties of continuously quasi-normed
spaces are introduced and their relationship to their analogues in real Banach spaces is discussed. It is shown that these properties lift from a continuously quasi-normed space $X$ to $L^p(\mu , X)$, for $0 < p < \infty $. Local versions of these properties and results are also considered.


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Additional Information

Patrick N. Dowling
Email: pndowling@miavx1.acs.muohio.edu

Zhibao Hu
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Address at time of publication: Department of Mathematics, El Paso Community College, P.O. Box 20500, Elpaso, Texas 79998
Email: davidhu@laguna.epcc.edu

Douglas Mupasiri
Email: mupasiri@math.uni.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01508-5
Keywords: Quasi-normed spaces, complex extreme points, complex strongly extreme points, analytic denting points
Received by editor(s): July 22, 1994
Article copyright: © Copyright 1996 American Mathematical Society