Sharp estimate on the resolvent of a finite-dimensional contraction

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Sharp estimate on the resolvent of a finite-dimensional contraction

Fouchet, Karine

Journal of mathematical analysis and applications, 08/2022, Volume: 512, Issue: 1

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We compute an asymptotic formula for the supremum of the resolvent norm ||(ζ−T)−1|| over |ζ|≥1 and contractions T acting on an n-dimensional Hilbert space, whose spectral radius does not exceed a given r∈(0,1). We prove that this supremum is achieved on the unit circle by an analytic Toeplitz matrix.

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