Compact composition operators on
Authors:
Joel H. Shapiro and Carl Sundberg
Journal:
Proc. Amer. Math. Soc. 108 (1990), 443-449
MSC:
Primary 47B38; Secondary 30D55, 47B05
DOI:
https://doi.org/10.1090/S0002-9939-1990-0994787-0
MathSciNet review:
994787
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The composition operator induced by a holomorphic self-map of the unit disc is compact on of the unit circle if and only if it is compact on the Hardy space
of the disc. This answers a question posed by Donald Sarason: it proves that Sarason's integral condition characterizing compactness on
is equivalent to the asymptotic condition on the Nevanlinna counting function which characterizes compactness on
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-0994787-0
Keywords:
Compact composition operator,
Nevanlinna counting function,
Riesz mass
Article copyright:
© Copyright 1990
American Mathematical Society