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A property for locally convex *-algebras related to property (T) and character amenability

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let C c ( G ) be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that ( C c ( G ) , ε G ) has property (FH) if and only if G has property (T). On...

A spectral mapping theorem for Banach modules

H. Seferoğlu (2003)

Studia Mathematica

Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then σ ( T μ ) = μ ̂ ( s p ( X ) ) ¯ for each measure μ in reg(M(G)), where T μ denotes the operator in B(X) defined by T μ x = μ ∘ x , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal I X = f ∈ L ¹ ( G ) | T f = 0 , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all...

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