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Compact composition operators on the Smirnov class |
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| Authors: | Jun Soo Choa Hong Oh Kim Joel H Shapiro |
| Institution: | Department of Mathematics Education, Sung Kyun Kwan University, Jongro-Gu, Seoul 110--745, Korea ; Department of Mathematics, KAIST, Taejon 305--701, Korea ; Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027 |
| 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  . 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. |
| Keywords: | Composition operator Smirnov class compact operator |
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