Normed spaces equivalent to inner product spaces and stability of functional equations

Let be a normed space. If is an equivalent norm coming from an inner product, then the original norm satisfies an approximate parallelogram law. Applying methods and results from the theory of stability of functional equations we study the reverse implication.

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Bibliographic Details
Published in:	Aequationes mathematicae Vol. 87; no. 1-2; pp. 147 - 157
Main Author:	Chmieliski, Jacek
Format:	Journal Article
Language:	English
Published:	Basel Springer Basel 01.03.2014 Springer Nature B.V
Subjects:	Analysis Approximation Combinatorics Equivalence Law Linear equations Mathematical analysis Mathematics Mathematics and Statistics Norms Parallelograms Quadratic programming Stability Texts Theorems quadratic functional equation 46C15 von Neumann–Jordan constant 46B03 approximate parallelogram law stability of functional equations 46B20 Normed space equivalent to inner product space 39B82
ISSN:	0001-9054, 1420-8903
Online Access:	Get full text
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