Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane

Year 2023, Volume: 6 Issue: 3, 128 - 134, 17.09.2023

Effie Oyugi Job Bonyo , David Ambogo

https://doi.org/10.33434/cams.1298613

Abstract

We construct a Ces\`{a}ro-type operator acting on Dirichlet space of the upper half plane using the approach of strongly continuous semigroups of composition operators on Banach spaces. We then determine the spectral and norm properties of the obtained Ces\`{a}ro-type operator.

Keywords

Ces\`{a}ro-type operator, Generator, One-parameter semigroup, Resolvent, Spectrum

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