The metrics of Hermitian holomorphic vector bundles and the similarity of Cowen-Douglas operators

Kui Ji () and Shanshan Ji ()
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Kui Ji: Hebei Normal University
Shanshan Ji: Hebei Normal University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 3, 736-749

Abstract: Abstract In this note, we investigate the similarity of Cowen-Douglas operators with index one in terms of the ratio of metrics of the corresponding holomorphic bundles. For the case of index two, we give some sufficient and necessary conditions for the similarity of $$M_{z}^{*}\oplus M_{z}^{*}$$ M z ∗ ⊕ M z ∗ by using the ratio of determinants of the metrics, where $$M_{z}$$ M z is the multiplication operator of weighted Bergman spaces.

Keywords: Cowen-Douglas operator; Similarity equivalence; Holomorphic vector bundle; Primary 47B13; 47B37; Secondary 47B48; 47L40 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00168-8

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