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A Borel extension approach to weakly compact operators on C 0 ( T )

Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

Let X be a quasicomplete locally convex Hausdorff space. Let T be a locally compact Hausdorff space and let C 0 ( T ) = { f T → I , f is continuous and vanishes at infinity } be endowed with the supremum norm. Starting with the Borel extension theorem for X -valued σ -additive Baire measures on T , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map u C 0 ( T ) → X to be weakly compact.

A C * -algebraic Schoenberg theorem

Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Donald W. Robinson (1984)

Annales de l'institut Fourier

Let 𝔄 be a C * -algebra, G a compact abelian group, τ an action of G by * -automorphisms of 𝔄 , 𝔄 τ the fixed point algebra of τ and 𝔄 F the dense sub-algebra of G -finite elements in 𝔄 . Further let H be a linear operator from 𝔄 F into 𝔄 which commutes with τ and vanishes on 𝔄 τ . We prove that H is a complete dissipation if and only if H is closable and its closure generates a C 0 -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...

A characterization of polynomially Riesz strongly continuous semigroups

Khalid Latrach, Martin J. Paoli, Mohamed Aziz Taoudi (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper we characterize the class of polynomially Riesz strongly continuous semigroups on a Banach space X . Our main results assert, in particular, that the generators of such semigroups are either polynomially Riesz (then bounded) or there exist two closed infinite dimensional invariant subspaces X 0 and X 1 of X with X = X 0 ⊕ X 1 such that the part of the generator in X 0 is unbounded with resolvent of Riesz type while its part in X 1 is a polynomially Riesz operator.

A characterization of the invertible measures

A. Ülger (2007)

Studia Mathematica

Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.

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