Boundary representations on $C^{\ast }$-algebras with matrix units
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- by Alan Hopenwasser PDF
- Trans. Amer. Math. Soc. 177 (1973), 483-490 Request permission
Abstract:
Let $\mathcal {A}$ be a ${C^\ast }$-algebra with unit, let $\mathcal {S}$ be a linear subspace of $\mathcal {A} \otimes {M_n}$ which contains the natural set of matrix units and which generates $\mathcal {A}$ as a ${C^\ast }$-algebra. Let $\mathcal {J}$ be the subset of $\mathcal {A}$ consisting of entries of matrices in $\mathcal {S}$. Then the boundary representations of $\mathcal {A} \otimes {M_n}$ relative to $\mathcal {S}$ are parametrized by the boundary representations of $\mathcal {A}$ relative to $\mathcal {J}$. Also, a nontrivial example is given of a subalgebra of a ${C^\ast }$-algebra which possesses exactly one boundary representation.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 177 (1973), 483-490
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9947-1973-0322522-2
- MathSciNet review: 0322522