Porous sets and lineability of continuous functions on locally compact groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:406

Article

Akbarbaglu, Ibrahim¹  Maghsoudi, Saeid¹  Seoane-Sepulveda, Juan B.² 

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

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

关键词: Continuous function;    sigma-c-lower porous set;    Locally compact group;    Convolution;    Lineability;    Spaceability;    Algebrability;   

DOI  :  10.1016/j.jmaa.2013.04.051

来源: Elsevier

【 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.

【 授权许可】

Free