Abstract:In this paper the necessary and sufficient conditions for the product of composition operators to be isometry are obtained on weighted Bergman space. With the help of a counter example we also proved that unlike on H 2 (D) and A 2 α (D), the composition operator on S 2 (D) induced by an analytic self map on D with fixed origin need not be of norm one. We have generalized the Schwartz's [4] well known result on A 2 α (D) which characterizes the almost multiplicative operator on H 2 (D).
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