Fredholmness of multiplication of a weighted composition operator with its adjoint on H 2 $H^{2}$ and A α 2 $A_{\alpha}^{2}$

Shaabani, Mahmood Haji

doi:10.1186/s13660-018-1615-0

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2021

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“…In [5] Shaabani gave the following characterization for invertibility of weighted composition operator on the weighted Bergman space which is instrumental in proving the results in the subsequent sections.…”

Section: Introductionmentioning

confidence: 98%

Isometries of the product of composition operators on weighted Bergman space

Gupta¹,

Yadav²

2021

Preprint

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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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Section: Introductionmentioning

confidence: 98%