Rocky Mountain Journal of Mathematics

The $C^*$-algebra generated by irreducibleToeplitz and composition operators

Massoud Salehi Sarvestani and Massoud Amini

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Abstract

We describe the $C^*$-algebra generated by an irreducible Toeplitz operator~$T_{\psi }$, with continuous symbol~$\psi $ on the unit circle $\mathbb {T}$, and finitely many composition operators on the Hardy space $H^2$ induced by certain linear fractional self-maps of the unit disc, modulo the ideal of compact operators $K(H^2)$. For specific automorphism-induced composition operators and certain types of irreducible Toeplitz operators, we show that the above $C^*$-al\-ge\-bra is not isomorphic to that generated by the shift and composition operators.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 4 (2017), 1301-1316.

Dates
First available in Project Euclid: 6 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1501984950

Digital Object Identifier
doi:10.1216/RMJ-2017-47-4-1301

Mathematical Reviews number (MathSciNet)
MR3689955

Zentralblatt MATH identifier
06790015

Subjects
Primary: 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22] 47B33: Composition operators

Keywords
$C^*$-algebra shift operator irreducible Toeplitz operator composition operator linear-fractional map automorphism of the unit disk

Citation

Sarvestani, Massoud Salehi; Amini, Massoud. The $C^*$-algebra generated by irreducibleToeplitz and composition operators. Rocky Mountain J. Math. 47 (2017), no. 4, 1301--1316. doi:10.1216/RMJ-2017-47-4-1301. https://projecteuclid.org/euclid.rmjm/1501984950


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