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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The factorization of a linear conjugate symmetric involution in Hilbert space

Author: James W. Moeller
Journal: Proc. Amer. Math. Soc. 94 (1985), 269-272
MSC: Primary 47B25
Erratum: Proc. Amer. Math. Soc. 97 (1986), 568.
MathSciNet review: 784177
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Abstract: Let $ X$ be a closed linear transformation whose domain is dense in the complex separable Hilbert space $ H$ and whose adjoint is denoted by $ {X^ * }$. The operator $ X$ is said to be conjugate symmetric if $ \Gamma (X) \subset \Gamma (Q{X^ * }Q)$, where $ \Gamma (X)$ represents the graph of $ X$ in $ H \otimes H$ and $ Q$ is a conjugation on $ H$. The main theorem in this note states that a conjugate symmetric linear involution $ X$ satisfies the operator equation $ X = Q{X^ * }Q$.

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Keywords: Hilbert space, closed linear transformation, conjugation operator
Article copyright: © Copyright 1985 American Mathematical Society