A characterization of bilateral operator weighted shifts being Cowen-Douglas operators

Ji, You Qing; Li, Juexian; Yang, Yihua

doi:10.1090/s0002-9939-01-06031-2

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Cited by 3 publications

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“…This follows from the famous similarity orbit theorem given by C. Apostol, L. A. Fialkow, D. A. Herrero and D. Voiculescu (See [2]). Subsequently, the Cowen-Douglas operator has been one of the important ingredients in the research of operator theory(cf [1,4,9,7,14,15,20,24,38,40,41,42,43,44,48,49,50]).…”

Section: Introductionmentioning

confidence: 99%

Similarity Classification of Cowen-Douglas Operators

Jiang¹

2004

Can. j. math.

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Abstract. Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be strongly irreducible, if A ′ (T), the commutant of A, has no non-trivial idempotent. An operator A in L(H) is said to be a Cowen-Douglas operator, if there exists Ω, a connected open subset of C, and n, a positive integer, such thatIn the paper, we give a similarity classification of strongly irreducible Cowen-Douglas operators by using the K 0 -group of the commutant algebra as an invariant.

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Section: Introductionmentioning

confidence: 99%

Similarity Classification of Cowen-Douglas Operators

Jiang¹

2004

Can. j. math.

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“…Operator weighted shifts were first introduced by A. Lambert [9], and have been studied by many authors (see for example [1], [6], [11], [7], and [8]). In the case when dim H = 1, they are exactly the scalar weighted shifts which have been widely studied.…”

Section: Introductionmentioning

confidence: 99%