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Topological structure of the space of composition operators on \(L^{\!\infty }\) of an unbounded, locally finite metric space

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Abstract

We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we characterize the compactness of differences of two such composition operators.

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Acknowledgements

We would like to thank Dr. Flavia Colonna (Professor of Mathematics, George Mason University) and Dr. Tushar Das (Professor of Mathematics, University of Wisconsin-La Crosse) for their many wonderful conversations and suggestions surrounding this manuscript. We would also like to express our appreciation to the referees for their thorough review of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Wisconsin-La Crosse, La Crosse, USA

    Robert F. Allen & Whitney George

  2. Department of Mathematics and Actuarial Science, North Central College, Naperville, USA

    Matthew A. Pons

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  1. Robert F. Allen
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  2. Whitney George
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  3. Matthew A. Pons
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Correspondence to Robert F. Allen.

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Allen, R.F., George, W. & Pons, M.A. Topological structure of the space of composition operators on \(L^{\!\infty }\) of an unbounded, locally finite metric space. Rend. Circ. Mat. Palermo, II. Ser 73, 715–729 (2024). https://doi.org/10.1007/s12215-023-00948-7

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