On commutativity of the commutant of strongly irreducible operator

Li, Jue-Xian

doi:10.1090/S0002-9939-2011-11118-3

On commutativity of the commutant of strongly irreducible operator
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Proc. Amer. Math. Soc. 140 (2012), 167-171 Request permission

Abstract:

In 2006, C. L. Jiang and Z. Y. Wang posed an open problem: If $T$ is a strongly irreducible operator, is ${\mathcal {A}}’(T)/\textrm {rad} {\mathcal A}’(T)$ commutative? They conjectured that the answer is positive. In this paper, to negatively answer their problem, a counterexample is given.

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