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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the normability of the intersection of $L_{p}$ spaces
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by Wayne C. Bell PDF
Proc. Amer. Math. Soc. 66 (1977), 299-304 Request permission

Abstract:

The set ${L_\omega } = \bigcap \nolimits _{p = 1}^\infty {{L_p}[0,1]}$ is not equal to ${L_\infty }[0,1]$ since ${L_\omega }$ contains the function $- \ln x$. Using the theory of ${L_p}$ spaces for finitely additive set functions developed by Leader [9] we will prove several necessary and sufficient conditions for the normability of a generalization of ${L_\omega }$. These include the equality and finite dimensionality of all the ${L_p}$ spaces, $p \geqslant 1$.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 299-304
  • MSC: Primary 46E99; Secondary 28A10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0482154-1
  • MathSciNet review: 0482154