Type II factors satisfying the spatial isomorphism conjecture. Academic Article

abstract

• This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94:38-54] that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N, and, moreover, the implementing unitary can be chosen to be close to the identity operator. This conjecture is known to be true for amenable von Neumann algebras, and in this paper, we describe classes of nonamenable factors for which the conjecture is valid. These classes are based on tensor products of the hyperfinite II(1) factor with crossed products of abelian algebras by suitably chosen discrete groups.

authors

• Smith, Roger

published proceedings

• Proc Natl Acad Sci U S A

author list (cited authors)

• Cameron, J., Christensen, E., Sinclair, A. M., Smith, R. R., White, S. A., & Wiggins, A. D.

citation count

• 3

complete list of authors

• Cameron, Jan||Christensen, Erik||Sinclair, Allan M||Smith, Roger R||White, Stuart A||Wiggins, Alan D

publication date

• December 2012

publisher

• Proceedings of the National Academy of Sciences  Publisher

published in

• Proceedings of the National Academy of Sciences of the United States of America  Journal

keywords

• Bounded Group Cohomology
• Kadison-kastler Stability
• Perturbations

PubMed Central ID

• 23184993

Digital Object Identifier (DOI)

• 10.1073/pnas.1217792109

URI

• https://hdl.handle.net/1969.1/181650

start page

• 20338

end page

• 20343

volume

• 109

issue

• 50

URL

• http%3A%2F%2Fdx.doi.org%2F10.1073%2Fpnas.1217792109