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Proceedings of the American Mathematical Society

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

 

 

The meaning of the Cauchy-Schwarz-Buniakovsky inequality


Author: Eduardo H. Zarantonello
Journal: Proc. Amer. Math. Soc. 59 (1976), 133-137
MSC: Primary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1976-0473931-0
MathSciNet review: 0473931
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Abstract: It is proved that a mapping $ T:X \to {X^{\ast}}$ from a topological real vector space into its dual satisfies the inequality $ \langle Ty,x\rangle \leqslant {\langle Tx,x\rangle ^{1/2}} \cdot {\langle Ty,y\rangle ^{1/2}}$ if and only if it is the restriction of a positively homogeneous subdifferential operator.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0473931-0
Keywords: Cauchy-Schwarz-Buniakovsky inequality, convex function, subdifferential, cyclically monotone operators
Article copyright: © Copyright 1976 American Mathematical Society