Geodesic
Toeplitz Operators on Bergman Spaces
Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 466-483

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a bounded, open, connected, non-empty subset of the complex plane C. We put the usual two dimensional (Lebesgue) area measure on G and consider the Hilbert space L 2(G) that consists of the complex-valued, measurable functions defined on G that are square integrable. The inner product on L 2(G) is given by the norm ‖h‖2 of a function h in L 2(G) is given by ‖h‖2 = (∫G |h|2)1/2.The Bergman space of G, denoted La 2(G), is the set of functions in L 2(G) that are analytic on G. The Bergman space La 2(G) is actually a closed subspace of L 2(G) (see [12 , Section 1.4]) and thus it is a Hilbert space.Let G denote the closure of G and let C(G) denote the set of continuous, complex-valued functions defined on G. 
Axler, Sheldon; Conway, John B.; McDonald, Gerard. Toeplitz Operators on Bergman Spaces. Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 466-483. doi: 10.4153/CJM-1982-031-1
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[1] 1. Adams, D. R. and Polking, J. C., The equivalence of two definitions of capacity, Proceedings A.M.S. 37 (1973), 529–534. Google Scholar

[2] 2. Ahlfors, L. V., Conformai invariants; Topics in geometric function theory (McGraw- Hill, 1973). Google Scholar

[3] 3. Ahlfors, L. and Beurling, A., Conformai invariants and function-theoretic null sets, Acta Math. (Uppsala) 83 (1950), 101–129. Google Scholar

[4] 4. Arveson, W., An invitation to C*-algebras, Springer-Verlag, Graduate Texts in Mathematics, Volume 39 (1976). Google Scholar

[5] 5. Berger, C. A. and Shaw, B. I., Self commutator s of multicyclic hyponormal operators are always trace class, Bulletin A.M.S. 79 (1973), 1193–1199. Google Scholar

[6] 6. Berger, C. A. and Shaw, B. I., Intertwining, analytic structure, and the trace norm estimate, in Proceedings of a conference on operator theory, Springer-Verlag, Lecture Notes in Mathematics, Volume 346 (1973). Google Scholar

[7] 7. Berger, C. A. and Shaw, B. I., Hyponormality: its analytic consequences, preprint. Google Scholar

[8] 8. Bergman, S., The kernel function and conformai mapping, American Mathematical Society, Mathematical Surveys, Number V, Second Edition (1970). Google Scholar

[9] 9. Carleson, L., Selected problems on exceptional sets (D. Van Nostrand, 1967). Google Scholar

[10] 10. Coburn, L. A., Singular integral operators and Toeplitz operators on odd spheres, Indiana Univ. Math. J. 23 (1973), 433–439. Google Scholar

[11] 11. Douglas, R. G., Banach algebra techniques in operator theory (Academic Press, 1972). Google Scholar

[12] 12. Epstein, B., Orthogonal families of analytic functions (Macmillan, 1965). Google Scholar

[13] 13. Gamelin, T. W., Uniform algebras (Prentice-Hall, 1969). Google Scholar

[14] 14. Garnett, J., Analytic capacity and measure, Springer Verlag, Lecture Notes in Mathematics, Volume 297 (1972). Google Scholar

[15] 15. Goldberg, S., Unbounded linear operators (McGraw-Hill, 1966). Google Scholar

[16] 16. Harvey, R. and Polking, J. C., A notion of capacity which characterizes removable singularities, Trans. A.M.S. 169 (1972), 183–195. Google Scholar

[17] 17. Hedberg, L. I., Approximation in the mean by analytic functions, Trans. A.M.S. 163 (1972), 157–171. Google Scholar

[18] 18. Jewell, N. P., Toeplitz operators on the Bergman spaces and in several complex variables, Proc. London Math. Soc. 41 (1980), 193–216. Google Scholar

[19] 19. Keough, G. E., Subnormal operators. Toeplitz operators, and spectral inclusion, Trans. A.M.S. 263 (1981), 125–135. Google Scholar

[20] 20. McDonald, G., Fredholm properties of a class of Toeplitz operators on the ball, Indiana Univ. Math. J. 26 (1977), 567–576. Google Scholar

[21] 21. McDonald, G. and Sundberg, C., Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), 595–611. Google Scholar

[22] 22. Pearcy, C. M., Some recent developments in operator theory, Conference board of the mathematical sciences, Regional conference series in mathematics 36 (1978). Google Scholar

[23] 23. Shields, A. L. and Wallen, L. J., The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777–788. Google Scholar

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