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) : μ̂ = 0 on Δ(M(G,ω))∖Δ(L¹(G,ω))}.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-3,
author = {S. J. Bhatt and H. V. Dedania},
title = {Weighted measure algebras and uniform norms},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {133-139},
zbl = {1110.43002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-3}
}
S. J. Bhatt; H. V. Dedania. Weighted measure algebras and uniform norms. Studia Mathematica, Tome 173 (2006) pp. 133-139. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-2-3/