Invariant subspaces for closed $*$-representations of $*$-algebras
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- by Itsuko Ikeda and Atsushi Inoue PDF
- Proc. Amer. Math. Soc. 116 (1992), 737-745 Request permission
Abstract:
The first purpose of this paper is to investigate the selfadjointness of $*$-subrepresentations of closed $*$-representations. The second purpose is to define the notion of selfadjoint vectors for any closed $*$-representation $\pi$ of a $*$-algebra $\mathcal {A}$ and to show that $\pi$ is decomposed into $\pi = \pi _1^S \oplus \pi _2^S$, where $\pi _1^S$ is a direct sum of cyclic selfadjoint representations of $\mathcal {A}$ and $\pi _2^S$ is a closed $*$-representation of $\mathcal {A}$ that does not have any nonzero selfadjoint vector.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 737-745
- MSC: Primary 47D40; Secondary 46K10, 46L99
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097345-7
- MathSciNet review: 1097345