Algebraic Properties of Toeplitz Operators on the Symmetrized Polydisk

Das, B. Krishna; Sau, Haripada

doi:10.1007/s11785-021-01108-4

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2022

2023

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Cited by 2 publications

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“…If, moreover, J is a contraction, we say that the module (H, S) is contractively embedded as a submodule of (K, R). A contractive module map J : H → K is called a canonical module map if (K, R) is minimal in the sense that there is no proper submodule of (K, R) containing (H, S) and reducing R and See [2,6] for the motivation of the definition above. Theorem 1.…”

Section: Introductionmentioning

confidence: 99%

Toeplitz operators and Hilbert modules on the symmetrized polydisc

Bhattacharyya¹,

Das²,

Sau³

2022

Int. J. Math.

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When is the collection of [Formula: see text]-Toeplitz operators with respect to a tuple of commuting bounded operators [Formula: see text], which has the symmetrized polydisc as a spectral set, nontrivial? The answer is in terms of powers of [Formula: see text] 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 [Formula: see text]-algebra generated by the commutant of [Formula: see text] and the commutant of its unitary extension [Formula: see text].

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Section: Introductionmentioning

confidence: 99%