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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Geometry of Banach spaces of functions associated with concave functions
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by Paul Hlavac and K. Sundaresan
Trans. Amer. Math. Soc. 215 (1976), 161-189
DOI: https://doi.org/10.1090/S0002-9947-1976-0388080-4

Abstract:

Let $(X,\Sigma ,\mu )$ be a positive measure space, and $\phi$ be a concave nondecreasing function on ${R^ + } \to {R^ + }$ with $\phi (0) = 0$. Let ${N_\phi }(R)$ be the Lorentz space associated with the function $\phi$. In this paper a complete characterization of the extreme points of the unit ball of ${N_\phi }(R)$ is provided. It is also shown that the space ${N_\phi }(R)$ is not reflexive in all nontrivial cases, thus generalizing a result of Lorentz. Several analytical properties of spaces ${N_\phi }(R)$, and their abstract analogues ${N_\phi }(E)$, are obtained when E is a Banach space.
References
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Bibliographic Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 215 (1976), 161-189
  • MSC: Primary 46E40; Secondary 46B05
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0388080-4
  • MathSciNet review: 0388080