Proceedings of the American Mathematical Society

Author(s): Jun Soo Choa; Hong Oh Kim; Joel H. Shapiro
Journal: Proc. Amer. Math. Soc. 128 (2000), 2297-2308.
MSC (1991): Primary 47B38; Secondary 30D55
Posted: December 8, 1999
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Abstract: We show that a composition operator on the Smirnov class

is compact if and only if it is compact on some (equivalently: every) Hardy space

for $0<p<\infty$ . Along the way we show that for composition operators on

both the formally weaker notion of boundedness, and a formally stronger notion we call metric compactness, are equivalent to compactness.

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Jun Soo Choa
Affiliation: Department of Mathematics Education, Sung Kyun Kwan University, Jongro-Gu, Seoul 110--745, Korea
Email: jschoa@yurim.skku.ac.kr

Hong Oh Kim
Affiliation: Department of Mathematics, KAIST, Taejon 305--701, Korea
Email: hkim@ftn.kaist.ac.kr

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