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Topological Structures of Generalized Volterra-Type Integral Operators

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Abstract

We study the generalized Volterra-type integral and composition operators acting on the classical Fock spaces. We first characterize various properties of the operators in terms of growth and integrability conditions which are simpler to apply than those already known Berezin type characterizations. Then, we apply these conditions to study the compact and Schatten \(\mathcal {S}_p\) class difference topological structures of the space of the operators. In particular, we proved that the difference of two Volterra-type integral operators is compact if and only if both are compact.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Western Norway University of Applied Sciences, Klingenbergvegen 8, 5414, Stord, Norway

    Tesfa Mengestie

  2. Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia

    Mafuz Worku

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  1. Tesfa Mengestie
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  2. Mafuz Worku
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Correspondence to Tesfa Mengestie.

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Mengestie, T., Worku, M. Topological Structures of Generalized Volterra-Type Integral Operators. Mediterr. J. Math. 15, 42 (2018). https://doi.org/10.1007/s00009-018-1080-5

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  • DOI: https://doi.org/10.1007/s00009-018-1080-5

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