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A note on states of von Neumann algebras

Allah-Bakhsh Thaheem (1979)

Aplikace matematiky

The author proves that on a von Neumann albebra (possibly of uncountable cardinality) there exists a family of states having mutually orthogonal supports (projections) converging to the identity operator.

Left quotients of a C*-algebra, III: Operators on left quotients

Lawrence G. Brown, Ngai-Ching Wong (2013)

Studia Mathematica

Let L be a norm closed left ideal of a C*-algebra A. Then the left quotient A/L is a left A-module. In this paper, we shall implement Tomita’s idea about representing elements of A as left multiplications: π p ( a ) ( b + L ) = a b + L . A complete characterization of bounded endomorphisms of the A-module A/L is given. The double commutant π p ( A ) ' ' of π p ( A ) in B(A/L) is described. Density theorems of von Neumann and Kaplansky type are obtained. Finally, a comprehensive study of relative multipliers of A is carried out.

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