On $W^{\ast }$ embedding of $AW^{\ast }$-algebras
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- by Diane Laison PDF
- Proc. Amer. Math. Soc. 35 (1972), 499-502 Request permission
Abstract:
An $A{W^ \ast }$-algebra N with a separating family of completely additive states and with a family $\{ {e_\alpha }:\alpha \in A\}$ of mutually orthogonal projections such that ${\operatorname {lub} _\alpha }{e_\alpha } = 1$ and ${e_\alpha }N{e_\alpha }$ is a ${W^ \ast }$-algebra for each $\alpha \in A$ is shown to have a faithful representation as a ring of operators. This gives a new and considerably shorter proof that a semifinite $A{W^ \ast }$-algebra with a separating family of completely additive states has a faithful representation as a ring of operators.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 499-502
- MSC: Primary 46K99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306928-8
- MathSciNet review: 0306928