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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 comment on free group factors

Narutaka Ozawa (2010)

Banach Center Publications

Let M be a finite von Neumann algebra acting on the standard Hilbert space L²(M). We look at the space of those bounded operators on L²(M) that are compact as operators from M into L²(M). The case where M is the free group factor is particularly interesting.

A F -algebras and topology of mapping tori

Igor Nikolaev (2015)

Czechoslovak Mathematical Journal

The paper studies applications of C * -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of A F -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding A F -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2 , 3 and 4 . In conclusion, we consider two numerical examples illustrating our main results.

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