Porous sets and lineability of continuous functions on locally compact groups

被引：4

作者：

Akbarbaglu, Ibrahim ^{[1
]}

Maghsoudi, Saeid ^{[1
]}

Seoane-Sepulveda, Juan B. ^{[2
]}

机构：

[1] Univ Zanjan, Dept Math, Zanjan 45195313, Iran

[2] Univ Complutense Madrid, Dept Anal Matemat, Fac Ciencias Matemat, E-28040 Madrid, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 406卷 / 01期

关键词：

Continuous function; sigma-c-lower porous set; Locally compact group; Convolution; Lineability; Spaceability; Algebrability; SPACES; ALGEBRABILITY; DICHOTOMIES; POROSITY;

D O I：

10.1016/j.jmaa.2013.04.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a non-compact locally compact group. In this paper we study the size of the set {(f, g) is an element of A x B : f * g is well-defined on G} where A and B are normed spaces of continuous functions on G. We also consider the problem of the spaceability of the set (C-0 (G) boolean AND (C-0(G) * C-0(G))) \ C-00 (G) and (among other results) we show that, for G = R-n, the above set is strongly c-algebrable (and, therefore, algebrable and lineable) with respect to the convolution product. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：211 / 218

页数：8

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