Weighted measure algebras and uniform norms

Bhatt, S. J. ; Dedania, H. V. (2006) Weighted measure algebras and uniform norms Studia Mathematica, 177 (2). pp. 133-139. ISSN 0039-3223

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Official URL: http://journals.impan.gov.pl/sm/Inf/177-2-3.html

Related URL: http://dx.doi.org/10.4064/sm177-2-3


Let ω be a weight on an LCA group G. Let M (G, ω) consist of the Radon measures µ on G such that ωµ is a regular complex Borel measure on G. It is proved that: (i) M(G, ω) is regular iff M(G, ω) has unique uniform norm property (UUNP) iff L1 (G, ω) has UUNP and G is discrete; (ii) M (G, ω) has a minimum uniform norm iff L1 (G, ω) has UUNP: (iii) M00 (G, ω) is regular iff M00 (G, ω) has UUNP iff L1 (G, ω) has UUNP, where M00 (G, ω) : = {µ ∈ M (G, ω) : µ^ - 0 on Δ (M(G, ω)) \ Δ (L1 (G, ω))}.

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