CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS

Lin, C.S.; Lin, C.S.

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.16 No.4

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CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2009, v.16 no.4, pp.359-367

Lin, C.S.

Lin,, C. (2009). CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 16(4), 359-367.

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Abstract

The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.

keywords: inner product space, Jordan-Neumann condition, parallelogram law, Ficken's condition, Oman's condition, law of cosines, Carlsson's condition, Day's codition

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Article Contents

Vol.16 No.4

CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics