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Fredholm and Semi-Fredholm Composition Operators on the Small Bloch-type Spaces

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Abstract

We characterize the Fredholm composition operators on the small Bloch-type spaces \({\mathcal{B}^{\alpha}}\), with 0 < α < 1, and give necessary and sufficient conditions for their semi-Fredholmness. For nontrivial composition operators the semi-Fredholmness is equivalent to the operator having a closed range, i.e. being bounded below. These properties have been characterized when the composition operator acts on the Bloch-type spaces \({\mathcal{B}^{\alpha}, \alpha \ge1}\). We extend some of those results, and give a few characterizations, for the leftover case of small Bloch-type spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    Nina Zorboska

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  1. Nina Zorboska
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Correspondence to Nina Zorboska.

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Nina Zorboska: Research supported in part by NSERC grant.

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Zorboska, N. Fredholm and Semi-Fredholm Composition Operators on the Small Bloch-type Spaces. Integr. Equ. Oper. Theory 75, 559–571 (2013). https://doi.org/10.1007/s00020-013-2042-8

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  • DOI: https://doi.org/10.1007/s00020-013-2042-8

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