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Porous sets and lineability of continuous functions on locally compact groups

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Akbarbaglu, Ibrahim and Maghsoudi, Saeid and Seoane-Sepúlveda, Juan B. (2013) Porous sets and lineability of continuous functions on locally compact groups. Journal of Mathematical Analysis and Applications, 406 (1). pp. 211-218. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X13003727


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Continuous function; sigma-c-lower porous set; Locally compact group; Convolution; Lineability; Spaceability; Algebrability
Subjects:Sciences > Mathematics > Algebra
ID Code:22587
Deposited On:26 Jul 2013 10:49
Last Modified:28 Nov 2016 08:55

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