Weighted measure algebras and uniform norms

• Autorzy: S. J. Bhatt , H. V. Dedania
• Języki publikacji: EN

Abstrakty

EN

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))}.

Kategorie tematyczne

• 43A20: L 1 -algebras on groups, semigroups, etc.
• 43A10: Measure algebras on groups, semigroups, etc.
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 177
• Numer: 2
• Strony: 133-139

Daty

wydano

2006

Twórcy

autor

S. J. Bhatt

• Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India

autor

H. V. Dedania

• Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India

Identyfikatory

DOI

10.4064/sm177-2-3