Compact composition operators

on the Smirnov class

 

Jun Soo Choa, Hong Oh Kim,

and Joel H. Shapiro

 

Proc. Amer. Math. Soc., 128 (2000) 2297--2308

 

Abstract: We show that a composition operator on the Smirnov class N^+ is compact if and only if it is compact on some (equivalently: every ) Hardy space H^p for p > 0 (and finite). Along the way we show that for composition operators on N^+, both the formally weaker notion of boundedness, and a formally stronger notion we call metric compactness, are equivalent to compactness.

 

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