Compact, nuclear, and Hilbert-Schmidt
composition operators on H^2
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Joel H. Shapiro and Peter D. Taylor
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Indiana Univ. Math.
J. 23 (1973/74) , 471--496
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| Abstract: My first paper on composition operators. It characterizes
the Hilbert-Schmidt composition operators and shows that non-finiteness
of the angular derivative is necessary for compactness. A sufficient
condition for compactness involving the angular derivative---much
strengthened in later papers---is proved, and these results are
used to give examples of compact and noncompact composition operators.
In particular, if the inducing map takes the unit disc into a
polygon inscribed in the unit circle, then the induced composition
operator is in every Schatten class. |
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