Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Analytic Toeplitz operators with automorphic symbol. II


Authors: M. B. Abrahamse and Joseph A. Ball
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] M. B. Abrahamse, Analytic Toeplitz operators with automorphic symbol, Proc. Amer. Math. Soc. 52 (1975), 297-302. MR 0405156 (53:8951)
  • [2] M. B. Abrahamse and R. G. Douglas, A class of subnormal operators related to multiply-connected domains, Advances in Math. 19 (1976), 1-43. MR 0397468 (53:1327)
  • [3] J. A. Ball, Hardy space expectation operators and reducing subspaces, Proc. Amer. Math. Soc. 47 (1975), 351-357. MR 50 #10887. MR 0358421 (50:10887)
  • [4] J. A. Deddens and T. K. Wong, The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc. 184 (1973), 261-273. MR 48 #2819. MR 0324467 (48:2819)
  • [5] A. Lubin, Isometries induced by composition operators and invariant subspaces, Illinois J. Math. 19 (1975), 424-427. MR 0415389 (54:3477)
  • [6] E. A. Nordgren, Reducing subspaces of analytic Toeplitz operators, Duke Math. J. 34 (1967), 175-181. MR 35 #7155. MR 0216321 (35:7155)
  • [7] -, Composition operators, Canad. J. Math. 20 (1968), 442-449. MR 36 #6961. MR 0223914 (36:6961)
  • [8] P. Rosenthal, Completely reducible operators, Proc. Amer. Math. Soc. 19 (1968), 826-830. MR 37 #6789. MR 0231234 (37:6789)
  • [9] W. Rudin, Pairs of inner functions on finite Riemann surfaces, Trans. Amer. Math. Soc. 140 (1969), 423-434. MR 39 #2968. MR 0241629 (39:2968)
  • [10] -, Some theorems on bounded analytic functions, Trans. Amer. Math. Soc. 78 (1955), 333-342. MR 16, 685. MR 0067192 (16:685b)
  • [11] D. Sarason, The $ {H^p}$ spaces of an annulus, Mem. Amer. Math. Soc. No. 56 (1965). MR 32 #6256. MR 0188824 (32:6256)
  • [12] E. L. Stout, On some algebras of analytic functions on finite open Riemann surfaces, Math. Z. 92 (1966), 366-379. Correction, ibid. 95 (1967), 403-404. MR 34 #358; 2913. MR 0200465 (34:358)
  • [13] J. E. Thomson, Intersection of commutants of analytic Toeplitz operators, Proc. Amer. Math. Soc. 52 (1975), 305-310. MR 0399927 (53:3765)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B35, 30A58

Retrieve articles in all journals with MSC: 47B35, 30A58


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0454714-4
Keywords: Toeplitz operator, automorphic function, modulus automorphic function, universal covering map, composition operator
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society