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2010 A Characterization of Inner Product Spaces Concerning an Euler-Lagrange Identity
Mohammad S. Moslehian, John M. Rassias
Commun. Math. Anal. 8(2): 16-21 (2010).

Abstract

In this paper we present a new criterion on characterization of real inner product spaces concerning the Euler-Lagrange type identity

$$\|r_2x_1-r_1x_2\|^2 + \|r_1x_1+r_2x_2\|^2=(r_1^2+r_2^2)(\|x_1\|^2+\|x_2\|^2)\,.$$

Citation

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Mohammad S. Moslehian. John M. Rassias. "A Characterization of Inner Product Spaces Concerning an Euler-Lagrange Identity." Commun. Math. Anal. 8 (2) 16 - 21, 2010.

Information

Published: 2010
First available in Project Euclid: 21 April 2010

zbMATH: 1194.46037
MathSciNet: MR2569953

Subjects:
Primary: 46B20 , 46C015 , 46C05

Keywords: characterization of inner product spaces , Day's condition , ‎inner product space , normed space , operator

Rights: Copyright © 2010 Mathematical Research Publishers

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Vol.8 • No. 2 • 2010
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