Kadison-Singer algebras, II: general case.
basic_science · Level V
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- Record sourced from PubMed, PMID 20185756.
- Also identified by DOI 10.1073/pnas.0914150107 and PMC identifier 2841906.
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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.