Open Access. Powered by Scholars. Published by Universities.®
Science and Technology Studies Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Science and Technology Studies
An Analytic Approach To Spectral Flow In Von Neumann Algebras, M-T Benameur, Alan L. Carey, John Phillips, Adam C. Rennie, Fyodor A. Sukochev, K P. Wojciechowski
An Analytic Approach To Spectral Flow In Von Neumann Algebras, M-T Benameur, Alan L. Carey, John Phillips, Adam C. Rennie, Fyodor A. Sukochev, K P. Wojciechowski
Faculty of Engineering and Information Sciences - Papers: Part A
The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm operators in a semifinite von Neumann algebra. The latter have continuous spectrum so that the notion of spectral flow turns out to be rather more difficult to deal with. However quite remarkably there is a uniform approach in which the proofs do not depend on discreteness of the spectrum of the operators in question. The first part of this paper …
Exel's Crossed Product And Relative Cuntz-Pimsner Algebras, Nathan Brownlowe, Iain Raeburn
Exel's Crossed Product And Relative Cuntz-Pimsner Algebras, Nathan Brownlowe, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We consider Exel's new construction of a crossed product of a $C^*$-algebra $A$ by an endomorphism $\alpha$. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be realised as a relative Cuntz-Pimsner algbera. We describe a necessary and sufficient condition for the canonical map from $A$ into the crossed product to be injective, and present several examples to demonstrate the scope of this result. We also prove a gauge-invariant uniqueness theorem for the crossed product.