Quadratic and quasi-quadratic functionals-Reference-Cited by-同舟云学术

Quadratic and quasi-quadratic functionals

Published:1993 Issue:4 Volume:119 Page:1105-1113
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Šemrl Peter

Abstract

In this note we show how Jordan ∗ {\ast } -derivations arise as a "measure" of the representability of quasi-quadratic functionals by sesquilinear ones. Our main result can be considered as an extension of the Jordan-von Neumann characterization of pre-Hilbert space.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1993-119-04/S0002-9939-1993-1158008-3/S0002-9939-1993-1158008-3.pdf

Reference12 articles.

1. Jordan derivations and quasibilinear forms;Davison, T. M. K.;Comm. Algebra,1984

2. The definition of a quadratic form;Gleason, Andrew M.;Amer. Math. Monthly,1966

3. On inner products in linear, metric spaces;Jordan, P.;Ann. of Math. (2),1935

4. The Cauchy functional equation and scalar product in vector spaces;Kurepa, Svetozar;Glasnik Mat.-Fiz. Astronom. Dru\v{s}tvo Mat. Fiz. Hrvatske Ser. II,1964

5. Quadratic and sesquilinear functionals;Kurepa, Svetozar;Glasnik Mat.-Fiz. Astronom. Dru\v{s}tvo Mat. Fiz. Hrvatske Ser. II,1965

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