Geometry of product spaces

被引：3
作者：
Sangeetha, M. Veena [1 ]
机构：
[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 503卷 / 01期
关键词：
Product spaces; Monotone norms; Full function spaces; k-Uniform rotundity; k-Uniform rotundity relative to every k-dimensional subspace; k-Rotundity; PSI-DIRECT SUMS; UNIFORM NON-SQUARENESS; BANACH-SPACES; MULTIDIMENSIONAL VOLUMES; STRICT CONVEXITY; ABSOLUTE NORMS; ROTUND;
D O I：
10.1016/j.jmaa.2021.125285
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the inheritance of some geometric properties in a class of normed subspaces of products of normed spaces. This class includes the standard p-direct sums for 1 <= p <= infinity. We obtain necessary conditions for a space of this class to be (1) nuniformly rotund, (2) n-uniformly rotund relative to every n-dimensional subspace and (3) n-rotund for some positive integer n. In each of the three cases, we identify a subclass such that the same conditions are sufficient for a member to have the corresponding property. (C) 2021 Elsevier Inc. All rights reserved.
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页数：23
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