A sharp bound for the functional calculus of ρ-contractions

Felix L. Schwenninger; Jens De Vries

doi:10.1090/proc/17346

A sharp bound for the functional calculus of ρ-contractions

Felix L. Schwenninger
, Jens De Vries

Research output: Contribution to journal › Article › Academic › peer-review

1 Citation (Scopus)

Abstract

Let A be a ρ-contraction and f a rational function mapping the closed unit disk into itself. With a new operator inequality for ρ-contractions, characterizing ρ-contractions for 1 ≤ ρ ≤ 2, we prove that (Formula presented.) We further show that this bound is sharp. This refines an estimate by Okubo–Ando and, for ρ = 2, is consistent with a result by Drury.

Original language	English
Pages (from-to)	4759-4768
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	153
Issue number	11
Early online date	10 Sept 2025
DOIs	https://doi.org/10.1090/proc/17346
Publication status	Published - Nov 2025

Keywords

2026 OA procedure
operator radius
unitary ρ-dilation
ρ-contraction
Functional calculus

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10.1090/proc/17346

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KW - operator radius

KW - unitary ρ-dilation

KW - ρ-contraction

KW - Functional calculus

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A sharp bound for the functional calculus of ρ-contractions

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A sharp bound for the functional calculus of ρ-contractions

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