Similarity classification of holomorphic curves

Jiang, Chunlan; Ji, Kui

doi:10.1016/j.aim.2007.03.015

Cited by 36 publications

(23 citation statements)

References 5 publications

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“…It is shown in [2] that if T is a CowenDouglas operator in B n (Ω), the map w → ker(T − w) is a holomorphic curve and the resulting bundle is E(T ). In this paper, we concentrate on unitary invariants of holomorphic curves, while we would like to mention the work of Jiang and Ji [12], who studied the similarity questions rather than unitary ones and some of their methods are related to ours.…”

Section: Preliminaries On Hermitian Vector Bundlesmentioning

confidence: 98%

On the double commutant of Cowen–Douglas operators

Chen

Douglas

Guo

2011

Journal of Functional Analysis

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Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V * (T ) consisting of operators commuting with both T and T * from a geometric viewpoint. We identify operators in V * (T ) with connection-preserving bundle maps on E(T ), the holomorphic Hermitian vector bundle associated to T . By studying such bundle maps, the structure of V * (T ) as well as information on reducing subspaces of T can be determined.

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Section: Preliminaries On Hermitian Vector Bundlesmentioning

confidence: 98%

On the double commutant of Cowen–Douglas operators

Chen

Douglas

Guo

2011

Journal of Functional Analysis

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“…The result can be viewed as an approximate Jordan Standard Theorem. In addition, Jiang and his cooperators [3,15,16] used K-theory and complex geometry to show that the ordered K 0 -groups of the commutant algebras of Cowen-Douglas operators form a complete set of similarity invariants.…”

Section: Introductionmentioning

confidence: 99%

The approximate Jordan forms of operators on Σ e 1 type Banach spaces

2011

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This paper studies the structure of operators on Σ 1 e type Banach spaces. It solves the problem of the small compact perturbations of operators with connected spectra. Namely, it shows that every operator with a connected spectrum on separable Σ 1 e type Banach spaces is a small compact perturbation of a strongly irreducible operator. Based on this result, this paper establishes the approximate Jordan forms of operators on Σ 1 e type Banach spaces with Schauder bases. KeywordsΣ 1 e type Banach spaces, strongly irreducible operators, operators with connected spectra, approximate Jordan forms MSC(2000): 46B20, 47A05 Citation: Zhang Y N, Lin L Q, Zhong H J. The approximate Jordan forms of operators on Σ 1 e type Banach spaces.

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“…Since then, the research with regard to strongly irreducible Cowen-Douglas operator has been greatly developed (see [8][9][10]12,14]). In particular, Jiang and his cooperators have used strongly irreducible operators and K 0 -groups to obtain the complete set of similarity invariants of Cowen-Douglas operators on complex separable infinitedimensional Hilbert spaces (see [11,13]). …”

Section: Introductionmentioning

confidence: 99%

Strongly irreducible operators and Cowen-Douglas operators on c 0, l p (1 ⩽ p < ∞)

Zhang

Zhong

2011

Front. Math. China

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This paper gives some sufficient conditions for the strongly irreducibility of operators which have the forms of upper triangular operator matrices on Banach spaces. Based on these results, strongly irreducible Cowen-Douglas operators of index n are constructed on c 0 , l p (1 p < ∞) for all 1 n ∞.Keywords Banach space, strongly irreducible operator, Cowen-Douglas operator, upper triangular operator matrice MSC 46B20, 47A05

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Similarity classification of holomorphic curves

Cited by 36 publications

References 5 publications

On the double commutant of Cowen–Douglas operators

On the double commutant of Cowen–Douglas operators

The approximate Jordan forms of operators on Σ e 1 type Banach spaces

Strongly irreducible operators and Cowen-Douglas operators on c 0, l p (1 ⩽ p < ∞)

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