Mathematics – Operator Algebras
Scientific paper
2003-01-22
Mathematics
Operator Algebras
59 pages, amstex
Scientific paper
We introduce the notion of finite right (respectively left) numerical index on a bimodule $X$ over C*-algebras A and B with a bi-Hilbertian structure. This notion is based on a Pimsner-Popa type inequality. The right (respectively left) index element of X can be constructed in the centre of the enveloping von Neumann algebra of A (respectively B). X is called of finite right index if the right index element lies in the multiplier algebra of A. In this case we can perform the Jones basic construction. Furthermore the C*--algebra of bimodule mappings with a right adjoint is a continuous field of finite dimensional C*-algebras over the spectrum of Z(M(A)), whose fiber dimensions are bounded above by the index. We show that if A is unital, the right index element belongs to A if and only if X is finitely generated as a right module. We show that bi-Hilbertian, finite (right and left) index C*-bimodules are precisely those objects of the tensor 2-C*-category of right Hilbertian C*-bimodules with a conjugate object, in the sense of Longo and Roberts, in the same category.
Kajiwara Toshihisa
Pinzari Claudia
Watatani Yasuo
No associations
LandOfFree
Jones index theory for Hilbert C*-bimodules and its equivalence with conjugation theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Jones index theory for Hilbert C*-bimodules and its equivalence with conjugation theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Jones index theory for Hilbert C*-bimodules and its equivalence with conjugation theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-74357