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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
MathSciNet review: 0454714
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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.

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Keywords: Toeplitz operator, automorphic function, modulus automorphic function, universal covering map, composition operator
Article copyright: © Copyright 1976 American Mathematical Society

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