Kadison-Singer Algebras: Hyperfinite Case
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA(2010)
摘要
A new class of operator algebras, Kadison-Singer algebras (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. A new invariant for the lattices is introduced to classify these algebras.
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关键词
Kadison-Singer lattice, reflexive algebra, triangular algebra, von Neumann algebra
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