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Proceedings of the American Mathematical Society

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

 
 

 

Orthogonality and nonlinear functionals on Banach spaces


Author: K. Sundaresan
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
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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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Keywords: Banach spaces, Hilbert spaces, orthogonality, additive functions
Article copyright: © Copyright 1972 American Mathematical Society