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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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Orthogonality and nonlinear functionals on Banach spaces
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by K. Sundaresan PDF
Proc. Amer. Math. Soc. 34 (1972), 187-190 Request permission

Abstract:

If B is a real Banach space and $x,y \in B$, then x is said to be orthogonal to $y\;(x \bot y)$ if $\left \| {x + \lambda y} \right \| \geqq \left \| x \right \|$ for all real numbers $\lambda$. A function $F:B \to E$, where E is a topological vector space, is said to be additive if it is continuous and $F(x + y) = F(x) + F(y)$ whenever $x \bot y$. The purpose of the present paper is to characterize additive functions.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 187-190
  • MSC: Primary 47A99
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0291835-X
  • MathSciNet review: 0291835