Analytic Toeplitz operators with automorphic symbol. II
HTML articles powered by AMS MathViewer
- by M. B. Abrahamse and Joseph A. Ball PDF
- Proc. Amer. Math. Soc. 59 (1976), 323-328 Request permission
Abstract:
For $\phi$ in ${H^\infty }$, let ${T_\phi }$ be the analytic Toeplitz operator with symbol $\phi$ and let $\{ {T_\phi }\} ’$ be the commutant of ${T_\phi }$. Two infinite Blaschke products $\phi$ and $\psi$, are exhibited such that $\{ {T_\phi }\} ’ \cap \{ {T_\psi }\} ’$ is not equal to $\{ {T_\theta }\} ’$ for any inner function $\theta$. Also, two questions on reducing subspaces of analytic Toeplitz operators are answered.References
- M. B. Abrahamse, Analytic Toeplitz operators with automorphic symbol, Proc. Amer. Math. Soc. 52 (1975), 297–302. MR 405156, DOI 10.1090/S0002-9939-1975-0405156-8
- M. B. Abrahamse and R. G. Douglas, A class of subnormal operators related to multiply-connected domains, Advances in Math. 19 (1976), no. 1, 106–148. MR 397468, DOI 10.1016/0001-8708(76)90023-2
- Joseph A. Ball, Hardy space expectation operators and reducing subspaces, Proc. Amer. Math. Soc. 47 (1975), 351–357. MR 358421, DOI 10.1090/S0002-9939-1975-0358421-7
- 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
- Arthur Lubin, Isometries induced by composition operators and invariant subspaces, Illinois J. Math. 19 (1975), 424–427. MR 415389
- Eric A. Nordgren, Reducing subspaces of analytic Toeplitz operators, Duke Math. J. 34 (1967), 175–181. MR 216321
- Eric A. Nordgren, Composition operators, Canadian J. Math. 20 (1968), 442–449. MR 223914, DOI 10.4153/CJM-1968-040-4
- Peter Rosenthal, Completely reducible operators, Proc. Amer. Math. Soc. 19 (1968), 826–830. MR 231234, DOI 10.1090/S0002-9939-1968-0231234-9
- Walter Rudin, Pairs of inner functions on finite Riemann surfaces, Trans. Amer. Math. Soc. 140 (1969), 423–434. MR 241629, DOI 10.1090/S0002-9947-1969-0241629-0
- Walter Rudin, Some theorems on bounded analytic functions, Trans. Amer. Math. Soc. 78 (1955), 333–342. MR 67192, DOI 10.1090/S0002-9947-1955-0067192-5
- Donald Sarason, The $H^{p}$ spaces of an annulus, Mem. Amer. Math. Soc. 56 (1965), 78. MR 188824
- E. L. Stout, On some algebras of analytic functions on finite open Riemann surfaces, Math. Z. 92 (1966), 366–379. MR 200465, DOI 10.1007/BF01112216
- 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
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 323-328
- MSC: Primary 47B35; Secondary 30A58
- DOI: https://doi.org/10.1090/S0002-9939-1976-0454714-4
- MathSciNet review: 0454714