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Operators in the Commutant of a Reductive Algebra

Robert L. Moore
Proceedings of the American Mathematical Society
Vol. 66, No. 1 (Sep., 1977), pp. 99-104
DOI: 10.2307/2041538
Stable URL: http://www.jstor.org/stable/2041538
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Operators in the Commutant of a Reductive Algebra
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Abstract

Let $\mathscr{A}$ be a reductive algebra. It is shown that there is a subspace $\mathscr{M}$ that reduces $\mathscr{A}$ and such that the commutant of $\mathscr{A}\mid\mathscr{M}$ is selfadjoint and the commutant of $\mathscr{A}\mid\mathscr{M}^\bot$ consists of hyporeductive operators. It is then shown that under a variety of conditions, if an operator $T$ is in a $\mathscr{A}'$, then $T^\ast$ is in $\mathscr{A}'$.

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