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Toeplitz operators and Hilbert modules on the symmetrized polydisc

Bhattacharyya, T and Krishna Das, B and Sau, H (2022) Toeplitz operators and Hilbert modules on the symmetrized polydisc. In: International Journal of Mathematics .

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Official URL: https://doi.org/10.1142/S0129167X22500768


When is the collection of S-Toeplitz operators with respect to a tuple of commuting bounded operators S = (S1,S2,..,Sd-1,P), which has the symmetrized polydisc as a spectral set, nontrivial? The answer is in terms of powers of P as well as in terms of a unitary extension. En route, the Brown-Halmos relations are investigated. A commutant lifting theorem is established. Finally, we establish a general result connecting the O-Algebra generated by the commutant of S and the commutant of its unitary extension R. © 2022 World Scientific Publishing Company.

Item Type: Journal Article
Publication: International Journal of Mathematics
Publisher: World Scientific
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 04 Jan 2023 09:41
Last Modified: 04 Jan 2023 09:41
URI: https://eprints.iisc.ac.in/id/eprint/78735

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