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Free Mutual Information for Two Projections

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Abstract

The present paper provides a proof of \(i^*(\mathbb {C}P+\mathbb {C}(I-P); \mathbb {C}Q+\mathbb {C}(I-Q))=-\chi _{{ orb}}(P,Q)\) for two projections P, Q without any extra assumptions. An analytic approach is adopted to the proof, based on a subordination result for the liberation process of symmetries associated with P, Q.

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Authors and Affiliations

  1. College of Business Administration, Qassim University, Buraydah, Saudi Arabia

    Tarek Hamdi

  2. Laboratoire d’Analyse Mathématiques et Applications LR11ES11, Université de Tunis El-Manar, Tunis, Tunisia

    Tarek Hamdi

Authors
  1. Tarek Hamdi
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Correspondence to Tarek Hamdi.

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Communicated by Daniel Aron Alpay.

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Hamdi, T. Free Mutual Information for Two Projections. Complex Anal. Oper. Theory 12, 1697–1705 (2018). https://doi.org/10.1007/s11785-018-0789-2

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  • DOI: https://doi.org/10.1007/s11785-018-0789-2

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