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arXiv · 2307.00508

Rational Cuntz states peak on the free disk algebra

Robert T. W. Martin·Eli Shamovich
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Abstract

We apply realization theory of non-commutative rational multipliers of the Fock space, or free Hardy space of square--summable power series in several non-commuting variables to the convex analysis of states on the Cuntz algebra. We show, in particular, that a large class of Cuntz states which arise as the `non-commutative Clark measures' of isometric NC rational multipliers are peak states for Popescu's free disk algebra in the sense of Clouâtre and Thompson.

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Robert T. W. Martin, Eli Shamovich. 2023-07-02. Rational Cuntz states peak on the free disk algebra. https://doi.org/10.1112/blms.13011

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