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November 2019 On the classification and geometry for Cowen–Douglas operators of high-rank case
Yingli Hou
Ann. Funct. Anal. 10(4): 472-482 (November 2019). DOI: 10.1215/20088752-2019-0005

Abstract

In this paper we introduce a subclass of Cowen–Douglas operators of high-rank case denoted by FBn,1(Ω). Each operator TFBn,1(Ω) is induced by one Cowen–Douglas operator with rank n, another Cowen–Douglas operator with rank 1, and an intertwining operator between them. By using this definition, we can construct plenty of Cowen–Douglas operators with high rank. By discussing the curvature of line bundle and second fundamental form of some rank 2 bundle and its subbundle, we give the unitary classification of operators in FBn,1(Ω) and we reduce the number of unitary invariants of this kind of operators from (n+1)2 to two.

Citation

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Yingli Hou. "On the classification and geometry for Cowen–Douglas operators of high-rank case." Ann. Funct. Anal. 10 (4) 472 - 482, November 2019. https://doi.org/10.1215/20088752-2019-0005

Information

Received: 10 December 2018; Accepted: 12 January 2019; Published: November 2019
First available in Project Euclid: 23 October 2019

zbMATH: 07126065
MathSciNet: MR4026361
Digital Object Identifier: 10.1215/20088752-2019-0005

Subjects:
Primary: 47B32, 47B35

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 4 • November 2019
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