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

共 50 条

[31] Arc components in locally compact groups are Borel sets
Hofmann, KH
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 65 (01) : 1 - 8
[32] PARTITIONS OF LOCALLY COMPACT-GROUPS IN NONMEASURABLE SETS
BERNARDI, MP
BONDIOLI, C
[J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1992, 6B (04): : 823 - 841
[33] SEPARABILITY OF ORBITS OF FUNCTIONS ON LOCALLY COMPACT GROUPS
PORTA, H
RUBEL, LA
SHIELDS, AL
[J]. STUDIA MATHEMATICA, 1973, 48 (01) : 89 - 94
[34] On dense-lineability of sets of functions on R
Aron, R. M.
Garcia-Pacheco, F. J.
Perez-Garcia, D.
Seoane-Sepulveda, J. B.
[J]. TOPOLOGY, 2009, 48 (2-4) : 149 - 156
[35] Sets of p-multiplicity in locally compact groups
Todorov, I. G.
Turowska, L.
[J]. STUDIA MATHEMATICA, 2015, 226 (01) : 75 - 93
[36] SPHERICAL MATRIX FUNCTIONS ON LOCALLY COMPACT GROUPS
SHINYA, H
[J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1974, 50 (5-6): : 368 - 373
[37] Approximation of functions on locally compact abelian groups
Ugulava, Duglas
[J]. GEORGIAN MATHEMATICAL JOURNAL, 2012, 19 (01) : 181 - 193
[38] Lineability and unbounded, continuous and integrable functions
Favaro, Vinicius V.
Pellegrino, Daniel
Raposo Jr, Anselmo
Ribeiro, Geivison
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (03)
[39] ON CERTAIN POROUS SETS IN THE ORLICZ SPACE OF A LOCALLY COMPACT GROUP
Akbarbaglu, Ibrahim
Maghsoudi, Saeid
[J]. COLLOQUIUM MATHEMATICUM, 2012, 129 (01) : 99 - 111
[40] Continuous bounded cohomology of locally compact groups - Introduction
Monod, N
[J]. CONTINUOUS BOUNDED COHOMOLOGY OF LOCALLY COMPACT GROUPS, 2001, 1758 : 1 - +

← 1 2 3 4 5 →