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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Partial Mielnik spaces and characterization of uniformly convex spaces


Authors: A. R. Blass and C. V. Stanojevic
Journal: Proc. Amer. Math. Soc. 55 (1976), 75-82
DOI: https://doi.org/10.1090/S0002-9939-1976-0394121-6
MathSciNet review: 0394121
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Abstract: We characterize uniform convexity of normed linear spaces in terms of a functional inequality generalizing Clarkson's inequality for $ {L_p}$ spaces. This inequality can be interpreted as saying that the unit sphere of the space carries a structure slightly weaker than a probability space in the sense of Mielnik. From this point of view, our result is analogous to an earlier characterization of inner product spaces. We also investigate briefly the abstract concept of partial probability space suggested by the main result.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0394121-6
Keywords: Uniformly convex spaces, Mielnik probability spaces
Article copyright: © Copyright 1976 American Mathematical Society