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Principal Functions for Bi-free Central Limit Distributions

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Abstract

We find the principal function of the completely non-normal operator l(v 1) + l(v 1)* + i(r(v 2) + r(v 2)*) on a subspace of the full Fock space \({\mathcal{F}}({\mathcal{H}})\) which arises from a bi-free central limit distribution. As an application, we find the essential spectrum of this operator.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Kenneth J. Dykema & Wonhee Na

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  1. Kenneth J. Dykema
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  2. Wonhee Na
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Correspondence to Kenneth J. Dykema.

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Research supported in part by NSF grant DMS–1202660.

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Dykema, K.J., Na, W. Principal Functions for Bi-free Central Limit Distributions. Integr. Equ. Oper. Theory 85, 91–108 (2016). https://doi.org/10.1007/s00020-015-2278-6

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  • DOI: https://doi.org/10.1007/s00020-015-2278-6

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