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Kadison–Singer algebras, II: General case

Kadison–Singer algebras, II: General case A new class of operator algebras, Kadison–Singer (KS-) algebras, is introduced. These highly noncommutative, non self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. It is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings of the National Academy of Sciences PNAS

Kadison–Singer algebras, II: General case

Proceedings of the National Academy of Sciences , Volume 107 (11): 4840 – Mar 16, 2010

Kadison–Singer algebras, II: General case

Proceedings of the National Academy of Sciences , Volume 107 (11): 4840 – Mar 16, 2010

Abstract

A new class of operator algebras, Kadison–Singer (KS-) algebras, is introduced. These highly noncommutative, non self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. It is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere.

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Publisher
PNAS
Copyright
Copyright ©2010 by the National Academy of Sciences
ISSN
0027-8424
eISSN
1091-6490
Publisher site
See Article on Publisher Site

Abstract

A new class of operator algebras, Kadison–Singer (KS-) algebras, is introduced. These highly noncommutative, non self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. It is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere.

Journal

Proceedings of the National Academy of SciencesPNAS

Published: Mar 16, 2010

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