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On a Special Case of the Herbert Stahl Theorem

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Abstract

The BMV conjecture states that for n ×  n Hermitian matrices A and B the function f A,B(t) = trace e tA+B is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is based on ingenious considerations related to Riemann surfaces of algebraic functions. In the present paper we give a purely “matrix” proof of the BMV conjecture for the special case rank A = 1. This proof is based on the Lie product formula for the exponential of the sum of two matrices and does not require complex analysis.

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  1. Department of Mathematics, The Weizmann Institute, 76100, Rehovot, Israel

    Victor Katsnelson

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  1. Victor Katsnelson
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Correspondence to Victor Katsnelson.

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Katsnelson, V. On a Special Case of the Herbert Stahl Theorem. Integr. Equ. Oper. Theory 86, 113–119 (2016). https://doi.org/10.1007/s00020-016-2309-y

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  • DOI: https://doi.org/10.1007/s00020-016-2309-y

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