Abstract
For an essentially normal operator T, it is shown that there exists a unilateral shift of multiplicity m in C*(T) if and only if γ(T)≠0 and γ(T)/m. As application, we prove that the essential commutant of a unilateral shift and that of a bilateral shift are not isomorphic as C*-algebras. Finally, we construct a natural C*-algebra ε + ε* on the Bergman space L ${}_{a}^{2}$ (Bn), and show that its essential commutant is generated by Toeplitz operators with symmetric continuous symbols and all compact operators.
Funding Statement
Supported by NSFC and Laboratory of Mathematics for Nonlinear Science at Fudan University.
Citation
Kunyu Guo. "Indices, characteristic numbers and essential commutants of Toeplitz operators." Ark. Mat. 38 (1) 97 - 110, March 2000. https://doi.org/10.1007/BF02384493
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