Direct decomposition of 𝜌-contraction and the unitary 𝜌-dilation

Hwa-Long Gau; Pei Yuan Wu

doi:10.1090/proc/17547

Direct decomposition of 𝜌-contraction and the unitary 𝜌-dilation

Proceedings of the American Mathematical Society 2026

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Authors: Hwa-Long Gau, Pei Yuan Wu

DOI: 10.1090/proc/17547

Cited by: 0

References: 4

Abstract

For ρ > 1 \rho >1 , let A A be a ρ \rho -contraction on a Hilbert space H H . Letting n ≥ 1 n\ge 1 and x x be a unit vector in H H , we show that (a) if ‖ A x ‖ = ‖ A 2 x ‖ = ⋯ = ‖ A n x ‖ ≡ c \|Ax\|=\|A^2x\|=\cdots =\|A^nx\|\equiv c , then c ≤ ρ ( ρ + n − 1 ) / n c\le \sqrt {\rho (\rho +n-1)/n} , and (b) ‖ A x ‖ = ‖ A

Fields of Study & Subjects

Holomorphic and Operator Theory Advanced Banach Space Theory Advanced Operator Algebra Research

Publication details

Journal / source: Proceedings of the American Mathematical Society
Volume: 154
Issue: 3
Pages: 1167–1180
Publication date: 15 January 2026
Language: EN

References 4