2021•arXiv (Cornell University)Open access

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

Anuradha Gupta, Geeta Yadav

Abstract

We obtain necessary and sufficient conditions for the composition and\nweighted composition operator and product of composition operators to be\nisometry and unitary on $H_{E}(\\xi).$ With the help of counter example we also\nprove that the product of two non isometric composition operator and weighted\ncomposition operator can be isometry on $H_{E}(\\xi)$. We also completely\ncharacterize the boundedness of generalized weighted composition operators on\n$H_{E}(\\xi).$\n

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