A characterization of $C^{\ast }$-subalgebras
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- by Jan A. van Casteren PDF
- Proc. Amer. Math. Soc. 72 (1978), 54-56 Request permission
Abstract:
Let A be a closed linear subspace of a ${C^\ast }$-algebra B. Adjoin, if necessary, the identity 1 to B. Then A is a ${C^\ast }$-subalgebra if and only if, for each x in A, the elements ${x^\ast }$ and $|x| + 1 - ||x| - 1|$ are in A. If 1 is in A, then A is a ${C^\ast }$-subalgebra if and only if $|x|$ is in A for each x in A. Here $|x|$ denotes the unique positive square root of ${x^\ast }x$ in B.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 54-56
- MSC: Primary 46L05; Secondary 46A40, 46K05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0503530-5
- MathSciNet review: 503530