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 \(M_{z}^{*}\oplus M_{z}^{*}\) by using the ratio of determinants of the metrics, where \(M_{z}\) is the multiplication operator of weighted Bergman spaces.
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Acknowledgements
The first author was supported by the National Natural Science Foundation of China (Grant No. 11922108); the second author was supported by the National Natural Science Foundation of China (Grant No. 12001159).
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Communicated by Gadadhar Misra.
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Ji, K., Ji, S. The metrics of Hermitian holomorphic vector bundles and the similarity of Cowen-Douglas operators. Indian J Pure Appl Math 53, 736–749 (2022). https://doi.org/10.1007/s13226-021-00168-8
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DOI: https://doi.org/10.1007/s13226-021-00168-8