On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups | Zendy

İbrahim Akbarbaglu | Zendy; S. Maghsoudi | Zendy

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On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

Author(s) -

İbrahim Akbarbaglu,

S. Maghsoudi

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/947908

Subject(s) - mathematics , locally compact space , locally convex topological vector space , locally compact group , haar measure , convolution (computer science) , topological group , space (punctuation) , topology (electrical circuits) , dual space , spectrum (functional analysis) , pure mathematics , lebesgue measure , lp space , algebraic number , regular polygon , topological space , lebesgue integration , banach space , combinatorics , mathematical analysis , linguistics , philosophy , physics , quantum mechanics , machine learning , artificial neural network , computer science , geometry

Let be a locally compact group with a fixed left Haar measure and Ω be a system of weights on . In this paper, we deal with locally convex space (,Ω) equipped with the locally convex topology generated by the family of norms (‖.‖,)∈Ω. We study various algebraic and topological properties of the locally convex space (,Ω). In particular, we characterize its dual space and show that it is a semireflexive space. Finally, we give some conditions under which (,Ω) with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum

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