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The norm spectrum in certain classes of commutative Banach algebras

H. S. Mustafayev (2011)

Colloquium Mathematicae

Let A be a commutative Banach algebra and let Σ A be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by σ ( f ) = f · a : a A ¯ Σ A , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.

The order structure of the space of measures with continuous translation

Gérard L. G. Sleijpen (1982)

Annales de l'institut Fourier

Let G be a locally compact group, and let B be a function norm on L 1 ( G ) loc such that the space L ( G , B ) of all locally integrable functions with finite B -norm is an invariant solid Banach function space. Consider the space L RUC ( G , B ) of all functions in L ( G , B ) of which the right translation is a continuous map from G into L ( G , B ) . Characterizations of the case where L RUC ( G , B ) is a Riesz ideal of L ( G , B ) are given in terms of the order-continuity of B on certain subspaces of L ( G ) . Throughout the paper, the discussion is carried out in the context...

The Poisson boundary of random rational affinities

Sara Brofferio (2006)

Annales de l’institut Fourier

We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all p -adic fileds.

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