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arXiv · 2505.12901

Sharp estimate on the resolvent of a finite-dimensional contraction

Karine Fouchet
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Abstract

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

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Karine Fouchet. 2025-05-19. Sharp estimate on the resolvent of a finite-dimensional contraction. https://doi.org/10.1016/j.jmaa.2022.126093

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