Weighted measure algebras and uniform norms

S. J. Bhatt, and H. V. Dedania. "Weighted measure algebras and uniform norms." Studia Mathematica 177.2 (2006): 133-139. <http://eudml.org/doc/286537>.

@article{S2006,
abstract = {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))\}.},
author = {S. J. Bhatt, H. V. Dedania},
journal = {Studia Mathematica},
keywords = {Banach algebra; Beurling algebra; Weighted measure algebra; unique uniform norm property; Gelfand space},
language = {eng},
number = {2},
pages = {133-139},
title = {Weighted measure algebras and uniform norms},
url = {http://eudml.org/doc/286537},
volume = {177},
year = {2006},
}

TY - JOUR
AU - S. J. Bhatt
AU - H. V. Dedania
TI - Weighted measure algebras and uniform norms
JO - Studia Mathematica
PY - 2006
VL - 177
IS - 2
SP - 133
EP - 139
AB - 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))}.
LA - eng
KW - Banach algebra; Beurling algebra; Weighted measure algebra; unique uniform norm property; Gelfand space
UR - http://eudml.org/doc/286537
ER -