Local completeness of operator algebras
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- by H. Behncke and J. Cuntz
- Proc. Amer. Math. Soc. 62 (1977), 95-100
- DOI: https://doi.org/10.1090/S0002-9939-1977-0428048-9
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Abstract:
A normed $\ast$-algebra $\mathcal {A}$ is called a local ${C^\ast }$-algebra, if all its maximal commutative $\ast$-subalgebras are ${C^\ast }$-algebras. It is shown that any local ${C^\ast }$-algebra dense in $\mathcal {K}(\mathcal {H})$, the algebra of compact operators on the Hilbert space $\mathcal {H}$ equals $\mathcal {K}(\mathcal {H})$. The same result holds also for local ${C^\ast }$-algebras dense in $A{W^\ast }$-algebras without a ${\text {II}_1}$ summand.References
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Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 95-100
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0428048-9
- MathSciNet review: 0428048