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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Extremal multilinear forms on Banach spaces
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by I. Sarantopoulos PDF
Proc. Amer. Math. Soc. 99 (1987), 340-346 Request permission


Suppose that $L$ is a continuous symmetric $m$-linear form defined on a complex Banach space $E$, and $\hat L$ is the associated homogeneous polynomial. If \[ || L || = ({m^m}/m!)|| {\hat L} ||,\] we prove that $E$ contains an almost isometric copy of $l_m^1$. In particular if $E$ is an $m$-dimensional space, then $E$ is isometrically isomorphic to $l_m^1$. We also prove that the only examples of such extremal $L$ which achieve their norm are suitable "extensions" of a known example given by Nachbin.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 340-346
  • MSC: Primary 46B20; Secondary 46G20
  • DOI:
  • MathSciNet review: 870797