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Articles 1 - 3 of 3
Full-Text Articles in Social and Behavioral Sciences
Kk-Theory And Spectral Flow In Von Neumann Algebras, J Kaad, R Nest, Adam C. Rennie
Kk-Theory And Spectral Flow In Von Neumann Algebras, J Kaad, R Nest, Adam C. Rennie
Faculty of Engineering and Information Sciences - Papers: Part A
We present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko(J).Given a semifinite spectral triple (A, H, D) relative to (N, t) with A separable, we construct a class [D] ? KK1(A, K(N)). For a unitary u ? A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u]A[D], and is simply related to the numerical spectral flow, and a refined C*-spectral flow.
Properties Preserved Under Morita Equivalence Of C*-Algebras, Astrid An Huef, Iain Raeburn, Dana Williams
Properties Preserved Under Morita Equivalence Of C*-Algebras, Astrid An Huef, Iain Raeburn, Dana Williams
Faculty of Engineering and Information Sciences - Papers: Part A
We show that important structural properties of C*-algebras and the muliplicity numbers of representations are preserved under Morita equivalence.
Extension Problems And Non-Abelian Duality For C*-Algebras, Astrid An Huef, S Kaliszewski, Iain Raeburn
Extension Problems And Non-Abelian Duality For C*-Algebras, Astrid An Huef, S Kaliszewski, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.