We study the C* -algebra generated by the Bergman operator with piecewise continuous coefficients in the Hilbert space L2 and extended by the Carleman rotation by an angle π. As a result, we obtain an efficient criterion for the operators from the indicated C* -algebra to be Fredholm operators.
Hilbert Space Unit Disk Compact Operator Toeplitz Operator Local Description
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M. Loaiza, “Algebras generated by the Bergman projection and operators of multiplication by piecewise continuous functions,” Integr. Equat. Operat. Theory, 46, 215–234 (2003).MathSciNetzbMATHGoogle Scholar
Yu. I. Karlovich, “Local-trajectory method for the study of invertibility of operators with discrete translation groups in С*-algebras,” Dokl. Akad. Nauk SSSR, 299, No. 3, 546–550 (1988).Google Scholar
Yu. I. Karlovich, “A local-trajectory method and isomorphism theorems for nonlocal С*-algebras,” Operat. Theory: Adv. Appl., 170, 137–166 (2006).MathSciNetzbMATHGoogle Scholar
I. B. Simonenko, “A new general method for the investigation of linear operator equations of the type of singular integral equations. I,” Izv. Akad. Nauk SSSR, Ser. Mat., 29, No. 3, 567–586 (1965).MathSciNetGoogle Scholar
I. B. Simonenko, “A new general method for the investigation of linear operator equations of the type of singular integral equations. II,” Izv. Akad. Nauk SSSR, Ser. Mat., 29, No. 4, 757–782 (1965).MathSciNetGoogle Scholar