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Displaying similar documents to “Statistical independence of operator algebras”

Pure states on Jordan algebras

Jan Hamhalter (2001)

Mathematica Bohemica

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We prove that a pure state on a C * -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application...

A note on states of von Neumann algebras

Allah-Bakhsh Thaheem (1979)

Aplikace matematiky

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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.