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2021•arXiv (Cornell University)Open access

Product isometry of generalized weighted composition operator on general weighted Hardy space

Anuradha Gupta, Yadav, Geeta

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Abstract

We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(ξ).$ With the help of counter example we also prove that the product of two non isometric composition operator and weighted composition operator can be isometry on $H_{E}(ξ)$. We also completely characterize the boundedness of generalized weighted composition operators on $H_{E}(ξ).$

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We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(ξ).$ With the help of counter example we also prove that the product of two non isometric composition operator and weighted composition operator can be isometry on $H_{E}(ξ)$. We also completely characterize the boundedness of generalized weighted composition operators on $H_{E}(ξ).$

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Available abstract

We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(ξ).$ With the help of counter example we also prove that the product of two non isometric composition operator and weighted composition operator can be isometry on $H_{E}(ξ)$. We also completely characterize the boundedness of generalized weighted composition operators on $H_{E}(ξ).$

Key concepts: Composition operator, Composition (language), Isometry (Riemannian geometry), Mathematics, Product (mathematics), Operator (biology), Hardy space, Unitary operator

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