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Weighted convolution algebras and their homomorphisms

Sandy Grabiner (1994)

Banach Center Publications

Weighted convolution algebras on subsemigroups of the real line [Book]

H. G. Dales, H. V. Dedania (2009)

Weighted Convolution Algebras without Bounded Approximate Identities.

M. Despic, F. Ghahramani, S. Grabiner (1995)

Mathematica Scandinavica

Weighted measure algebras and uniform norms

S. J. Bhatt, H. V. Dedania (2006)

Studia Mathematica

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))}.

When is there a discontinuous homomorphism from L¹(G)?

Volker Runde (1994)

Studia Mathematica

Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.