1,721,172 research outputs found
Automorphisms of the UHF algebra that do not extend to the Cuntz algebra
No full textAbstractThe automorphisms of the canonical core UHF subalgebra ℱn of the Cuntz algebra 𝒪n do not necessarily extend to automorphisms of 𝒪n. Simple examples are discussed within the family of infinite tensor products of (inner) automorphisms of the matrix algebras Mn. In that case, necessary and sufficient conditions for the extension property are presented. Also addressed is the problem of extending to 𝒪n the automorphisms of the diagonal 𝒟n, which is a regular maximal abelian subalgebra with Cantor spectrum. In particular, it is shown that there exist product-type automorphisms of 𝒟n that do not extend to (possibly proper) endomorphisms of 𝒪n.</jats:p
Fourier theory and C*-algebras
Full text linkWe discuss a number of results concerning the Fourier series of elements in reduced
twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products
associated to twisted actions of discrete groups on unital C∗-algebras. A major part of
the article gives a review of our previous work on this topic, but some new results are also
included
The Fourier–Stieltjes algebra of a C*-dynamical system
Full text linkIn analogy with the Fourier–Stieltjes algebra of a group, we associate to a unital discrete
twisted C∗-dynamical system a Banach algebra whose elements are coefficients of
equivariant representations of the system. Building upon our previous work, we show
that this Fourier–Stieltjes algebra embeds continuously in the Banach algebra of completely
bounded multipliers of the (reduced or full) C∗-crossed product of the system.
We introduce a notion of positive definiteness and prove a Gelfand–Raikov type theorem
allowing us to describe the Fourier–Stieltjes algebra of a system in a more intrinsic way.
We also propose a definition of amenability for C∗-dynamical systems and show that it
implies regularity. After a study of some natural commutative subalgebras, we end with
a characterization of the Fourier–Stieltjes algebra involving C∗-correspondences over the
(reduced or full) C∗-crossed product
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