Characterization of Inner Product Spaces

被引：0

作者：

Sain D. ^{[1
]}

Paul K. ^{[1
]}

Debnath L. ^{[2
]}

机构：

[1] Department of Mathematics, Jadavpur University, Kolkata

[2] Department of Mathematics, The University of Texas-Pan American, 1201 West University Drive, Edinburg, 78539, TX

来源：

International Journal of Applied and Computational Mathematics | 2015年 / 1卷 / 4期

关键词：

Best approximation; Best coapproximation; Inner product space; Strictly convex space; Strong orthogonality;

D O I：

10.1007/s40819-015-0036-8

中图分类号：

学科分类号：

摘要：

We prove that the existence of best coapproximation to any element of the normed linear space out of any one dimensional subspace and its coincidence with the best approximation to that element out of that subspace characterizes a real inner product space of dimension > 2. We conjecture that a finite dimensional real smooth normed space of dimension > 2 is an inner product space iff given any element on the unit sphere there exists a strongly orthonormal Hamel basis in the sense of Birkhoff–James containing that element. This is substantiated by our result on the spaces (R n , ‖. ‖ p ). © 2015, Springer India Pvt. Ltd.

引用

页码：599 / 606

页数：7

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