Weighted (LF)-spaces of measurable functions

Wengenroth, Jochen

doi:10.1007/bf03322536

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2011

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“…In this paper, we equip the space L p G, Ω with the natural locally convex topology generated by the family of norms • p,ω , where ω runs through Ω. For a similar study in other contexts, see [6][7][8] . We investigate certain algebraic and topological properties of the locally convex space L p G, Ω .…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

Akbarbaglu

Maghsoudi

2011

Abstract and Applied Analysis

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

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Section: Introductionmentioning

confidence: 99%