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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.16 No.4

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CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS

CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2009, v.16 no.4, pp.359-367
Lin, C.S. (DEPARTMENT OF MATHEMATICS, BISHOP'S UNIVERSITY)
Lin, C.S.. (2009). CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS, 16(4), 359-367.

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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한국수학교육학회지시리즈B:순수및응용수학

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