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Toeplitz operators and Hilbert modules on the symmetrized polydisc
Journal
International Journal of Mathematics
ISSN
0129167X
Date Issued
2022-10-01
Author(s)
Bhattacharyya, Tirthankar
Krishna Das, B.
Sau, Haripada
Abstract
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 C*-algebra generated by the commutant of S and the commutant of its unitary extension R.
Volume
33
Publication link
Subjects