Abstract of a paper by Mohammad Sal Moslehian and John M. Rassias
This is an announcement for the paper "A characterization of inner product spaces" by Mohammad Sal Moslehian and John M. Rassias. Abstract: In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \|\cdot\|)$ is an inner product space if $$\sum_{\varepsilon_i \in \{-1,1\}} \left\|x_1 + \sum_{i=2}^k\varepsilon_ix_i\right\|^2=\sum_{\varepsilon_i \in \{-1,1\}} \left(\|x_1\| + \sum_{i=2}^k\varepsilon_i\|x_i\|\right)^2\,,$$ for some positive integer $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Conversely, if $(X, \|\cdot\|)$ is an inner product space, then the equality above holds for all $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Archive classification: math.FA math.CA Mathematics Subject Classification: Primary 46C15, Secondary 46B20, 46C05 Remarks: 8 Pages, to appear in Kochi J. Math. (Japan) Submitted from: moslehian@ferdowsi.um.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.0079 or http://arXiv.org/abs/1009.0079
participants (1)
-
alspach@fourier.math.okstate.edu