CHARACTERIZATIONS OF INNER PRODUCT SPACES BY INEQUALITIES INVOLVING SEMI-INNER PRODUCT

被引：0

作者：

Wojcik, Pawel ^{[1
]}

机构：

[1] Pedag Univ Cracow, Inst Math, PL-30084 Krakow, Poland

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2015年 / 18卷 / 03期

关键词：

Semi-inner product; characterization of inner product spaces; inequality; projection; smoothness; norm derivative;

D O I：

10.7153/mia-18-64

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the notion of semi-inner product in normed spaces, in this paper we provide some new characterizations of inner product spaces. We answer a question posed by Dragomir, whether the property (N) is characteristic for inner product spaces. We show that the space X is of (N)-type if and only if the norm in X comes from an inner product.

引用

页码：879 / 885

页数：7

共 7 条

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[3] Dragomir SS., 2004, SEMIINNER PRODUCTS A
[4] GILES JR, 1967, T AM MATH SOC, V129, P436
[5] Kakutani S., 1939, Jpn. J. Math., V16, P93
[6] Lumer G., 1961, T AM MATH SOC, V100, P29, DOI [10.1090/S0002-9947-1961-0133024-2, DOI 10.1090/S0002-9947-1961-0133024-2]
[7] Milicic P. M., 1987, Mat. Vesnik., V39, P325

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