Similarity of quotient Hilbert modules in the Cowen–Douglas class

Authors

Kui Ji, Hebei Normal University
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

European Journal of Mathematics

Abstract

We consider similarity and quasi-affinity problems for Hilbert modules in the Cowen–Douglas class associated with the complex geometric objects, the hermitian anti-holomorphic vector bundles and curvatures. Given a “simple” rank one Cowen–Douglas Hilbert module M, we find necessary and sufficient conditions for a class of Cowen–Douglas Hilbert modules satisfying some positivity conditions to be similar to [InlineEquation not available: see fulltext.] We also show that under certain uniform bound condition on the anti-holomorphic frame, a Cowen–Douglas Hilbert module is quasi-affinity to a submodule of the free module [InlineEquation not available: see fulltext.].

First Page

1331

Last Page

1351

DOI

10.1007/s40879-018-0297-y

Publication Date

12-1-2019

Comments

Open Access, Green

Recommended Citation

Ji, Kui and Sarkar, Jaydeb, "Similarity of quotient Hilbert modules in the Cowen–Douglas class" (2019). Journal Articles. 592.
https://digitalcommons.isical.ac.in/journal-articles/592