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Decomposability and the cyclic
behavior
of parabolic composition operators
Joel H. Shapiro
In: Recent Progress in Functional
Analysis, Proceedings of the International Functional Analysis
Meeting on the Occasion of the 70th Birthday of Professor Manuel
Valdivia, Valencia, Spain, July 3-7, 2000, K.D. Bierstedt, J.
Bonet, M. Maestre, J. Schmets (ed.), North-Holland Math. Studies,
2001.
Abstract: In
this paper I study composition operators induced by linear fractional
selfmaps of the unit disc that are parabolic, but not onto. I
show that such maps induce composition operators on the Hardy
space H^p (1 <= p < infinity) that are decomposable.
This result, the spectral properties of the operators being
studied, and a recent result of Len and Vivien Miller, shows
that such composition operators are not supercyclic. This
work generalizes previous work of Gallardo and Montes, who proved
the non-supercyclicity result, by different methods, for p=2,
and it complements work of Robert Smith who proved decomposability
for composition operators induced by parabolic automorphisms
("onto parabolics"). The paper features a significant
expository component that makes it mostly self-contained.
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