Quadratic functional equation and inner product spaces. (English) Zbl 0836.39006
The aim of the paper is to characterize inner product spaces as those in which the square of the norm satisfies some functional equations. The author considers five such equations. Actually, the equations are solved in general, and in some important cases it is noticed that their only solutions are quadratic functionals (i.e. functionals satisfying the Jordan-von Neumann identity).
Reviewer: M.Sablik (Katowice)
MSC:
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 39B22 | Functional equations for real functions |
| 15A63 | Quadratic and bilinear forms, inner products |
Keywords:
characterization; inner product spaces; functional equations; quadratic functionals; Jordan-von Neumann identityReferences:
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