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A double commutant theorem for conjugate selfadjoint operators

Author: James W. Moeller
Journal: Proc. Amer. Math. Soc. 83 (1981), 506-508
MSC: Primary 47B47; Secondary 47C05
MathSciNet review: 627679
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Abstract: Let $ A$ be a bounded linear transformation on the complex separable Hilbert space $ H$. If there is a conjugation $ Q$ on $ H$ such that $ A = Q{A^*}Q$, we say that $ A$ is conjugate selfadjoint. In this note we examine commutativity properties of conjugate selfadjoint operators which possess cyclic vectors.

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Keywords: Hilbert space, linear transformation, commutant, cyclic vector
Article copyright: © Copyright 1981 American Mathematical Society

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