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Proceedings of the American Mathematical Society

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Invariant subspaces for closed $ *$-representations of $ *$-algebras


Authors: Itsuko Ikeda and Atsushi Inoue
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1097345-7
Keywords: Closed (selfadjoint, integrable) representation selfadjoint (integrable, bounded) vector
Article copyright: © Copyright 1992 American Mathematical Society