Sharp estimate on the resolvent of a finite-dimensional contraction

2025/05/19 by Fouchet, Karine
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.12901

Abstract

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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