Abstract
In [2], Axler, Conway and McDonald, discuss the essential spectrum of Toeplitz operator, with continuous symbol, on the unweighted Bergman space. This paper extends their results to the weighted Bergman space, where the weight and its logarithm are assumed to be locally integrable.
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S. Axler. Multiplication operators on Bergman spaces, J. reine angew Math 336 (1982), 26–44.
S. Axler, J. Conway and G. McDonald. Toeplitz operators on Bergman spaces, Canadian J. Math 34 (1982), 466–483.
J. E. Brennan. Invariant subspaces and weighted polynomial approximation, Ark. Math 11, 167–189.
C. A. Berger and B. I. Shaw. Hyponormality: its analytic consequences. (Preprint)
J. B. Conway. Subnormal operators, Research Notes in Mathematics 51.
M. J. Cowen and R. G. Douglas. Complex geometry and operator theory, Acta Math. 141, 187–261.
J. Garnett. Analytic capacity and measure, Springer-Verlag, Lectures Notes in Mathematics, 297 (1972).
D. Hadwin and E. Nordgren. The Berger-Shaw Theorem, to appear in Proc. Amer. Math. Soc.
R. F. Olin and J. E. Thomson. Algebras generated by a subnormal operator Trans. of the Amer. Math. Soc. 271, #1, (1982), 299–311.
M. A. Subin. Factorization of parameter — dependent matrix functions in normal rings and certain related questions in the theory of Noetherian operators, translation, Math U.S.S.R. sb. 2, 543–560.
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This paper represents part of the author's Ph.D. thesis, written at Indiana University under the direction of Professor John B. Conway.
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Elias, N. Toeplitz operators on weighted Bergman spaces. Integr equ oper theory 11, 310–331 (1988). https://doi.org/10.1007/BF01202076
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DOI: https://doi.org/10.1007/BF01202076