The commutants of certain analytic Toeplitz operators
HTML articles powered by AMS MathViewer
- by James E. Thomson
- Proc. Amer. Math. Soc. 54 (1976), 165-169
- DOI: https://doi.org/10.1090/S0002-9939-1976-0388156-7
- PDF | Request permission
Abstract:
In this paper we characterize the commutants of two classes of analytic Toeplitz operators. We show that if $F$ in ${H^\infty }$ is univalent and nonvanishing, the $\{ {T_{{F^2}}}\} ’ = \{ {T_z}\} ’$. When $\varphi$ is the product of two Blaschke factors, we characterize $\{ {T_\varphi }\} ’$ in terms of algebraic combinations of Toeplitz and composition operators.References
- I. N. Baker, James A. Deddens, and J. L. Ullman, A theorem on entire functions with applications to Toeplitz operators, Duke Math. J. 41 (1974), 739–745. MR 355046
- Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89–102. MR 160136, DOI 10.1007/978-1-4613-8208-9_{1}9
- James A. Deddens and Tin Kin Wong, The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc. 184 (1973), 261–273. MR 324467, DOI 10.1090/S0002-9947-1973-0324467-0
- Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- Eric A. Nordgren, Reducing subspaces of analytic Toeplitz operators, Duke Math. J. 34 (1967), 175–181. MR 216321
- John V. Ryff, Subordinate $H^{p}$ functions, Duke Math. J. 33 (1966), 347–354. MR 192062
- James E. Thomson, Intersections of commutants of analytic Toeplitz operators, Proc. Amer. Math. Soc. 52 (1975), 305–310. MR 399927, DOI 10.1090/S0002-9939-1975-0399927-4
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 165-169
- DOI: https://doi.org/10.1090/S0002-9939-1976-0388156-7
- MathSciNet review: 0388156