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2013 A Characterization Of The Inner Product Spaces Involving Trigonometry
‎Mihai Monea, Mihai Opincariu, Marian Stroe, Dan Ştefan Marinescu
Ann. Funct. Anal. 4(1): 109-113 (2013). DOI: 10.15352/afa/1399899840

Abstract

‎In this paper we will give a new characterization of the inner product space which use the trigonometry‎. ‎We conclude that a normed space $\left( X,\left\Vert \cdot \right\Vert \right)$ is an inner product space if and only if there exists $\alpha\in\mathbb{R}\backslash \pi\mathbb{Q}$ so that‎ ‎$$\left\Vert x\cos\alpha‎ + ‎y\sin\alpha\right\Vert^{2}+\left\Vert y\cos\alpha‎ - ‎x\sin\alpha\right\Vert^{2}=\left\Vert x\right\Vert^{2}+\left\Vert y\right\Vert^{2},$$‎ ‎for any $x,y\in X$‎.

Citation

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‎Mihai Monea. Mihai Opincariu. Marian Stroe. Dan Ştefan Marinescu. "A Characterization Of The Inner Product Spaces Involving Trigonometry." Ann. Funct. Anal. 4 (1) 109 - 113, 2013. https://doi.org/10.15352/afa/1399899840

Information

Published: 2013
First available in Project Euclid: 12 May 2014

zbMATH: 1273.46014
MathSciNet: MR3004214
Digital Object Identifier: 10.15352/afa/1399899840

Subjects:
Primary: 46C15
Secondary: 46B20

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.4 • No. 1 • 2013
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