Abstract
We define . In this paper, we characterize composition operators and their adjoints which belong to , where the maps are linear fractional selfmaps of the open unit disk into itself. If is an automorphism of or , then the case for is precisely when it is normal. When , we also prove that if , then either or , which implies that the only binormal composition operators with and are normal. Moreover, we show that if and is not normal, then implies that and is neither real nor purely imaginary, while ensures that and is real. Finally, we study composition operators in where is an analytic selfmap into . In particular, this operator has the single-valued extension property.
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