Two mappings related to semi-inner products and their applications in geometry of normed linear spaces

被引：0
|
作者：
Dragomir S.S. [1 ]
Koliha J.J. [2 ]
机构：
[1] Sch. of Commun. and Informatics, Victoria University of Technology, MCMC, Melbourne, Vic. 8001
[2] Dept. of Mathematics and Statistics, University of Melbourne, Parkville
来源：
Applications of Mathematics | 2000年 / 45卷 / 05期
关键词：
Best approximants; Birkhoff orthogonality; Lower and upper semi-inner product; Schwarz inequality; Semi-inner products; Smooth normed spaces;
D O I：
10.1023/A:1022268627299
中图分类号：
学科分类号：
摘要：
In this paper we introduce two mappings associated with the lower and upper semi-inner product (·, ·)i and (·, ·)s and with semi-inner products [·, ·] (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.
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页码：337 / 355
页数：18
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