New York Journal of Mathematics
Volume 28 (2022), 868-883


Sameer Chavan and Archana Morye

The eigensheaf of an operator

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Published: June 6, 2022.
Keywords: Cowen-Douglas class, Toeplitz operator, holomorphic vector bundle, locally free, cokernel sheaf.
Subject: Primary 47B13, 47B35; Secondary 55Rxx.

If a bounded linear opertor T on a Hilbert space H lies in the Cowen-Douglas class, then its eigensheaf is locally free, but not conversely. We obtain a model for operators whose eigensheaves are locally free. We describe the eigensheaves for certain coanalytic Toeplitz operators, we show that the map from an operator to its eigensheaf is a functor from the category of bounded linear operators on Hilbert space to the category of Hilbert space-valued analytic sheaves, and we discuss relation between the eigensheaf of an operator and the sheaf that Putinar associates to an operator.


The work of the second author was supported through UGC SAP (DSA 1).

Author information

Sameer Chavan:
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur, India


Archana Morye:
School of Mathematics and Statistics
University of Hyderabad, India