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Classification of quasi-homogeneous holomorphic curves and operators in the Cowen-Douglas class

Jiang, Chunlan and Ji, Kui and Misra, Gadadhar (2017) Classification of quasi-homogeneous holomorphic curves and operators in the Cowen-Douglas class. In: JOURNAL OF FUNCTIONAL ANALYSIS, 273 (9). pp. 2870-2915.

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Official URL: http://doi.org/10.1016/j.jfa.2017.06.015


In this paper we study quasi-homogeneous operators, which include the homogeneous operators, in the Cowen-Douglas class. We give two separate theorems describing canonical models (with respect to equivalence under unitary and invertible operators, respectively) for these operators using techniques from complex geometry. This considerably extends the similarity and unitary classification of homogeneous operators in the Cowen-Douglas class obtained recently by the last author and A. Koranyi. In a significant generalization of the properties of the homogeneous operators, we show that quasi-homogeneous operators are irreducible and determine which of them are strongly irreducible. Applications include the equality of the topological and algebraic K-group of a quasi-homogeneous operator and an affirmative answer to a well-known question of Halmos. (C) 2017 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 13 Oct 2017 04:53
Last Modified: 13 Oct 2017 04:53
URI: http://eprints.iisc.ac.in/id/eprint/58002

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