科研之友
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摘要
Let H be a complex seperable Hilbert space and L(H) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/ rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.
