Strongly Kreiss Bounded Operators in UMD Banach Spaces

2023/11/02 by Chenxi Deng, Deng, Chenxi, Emiel Lorist +3
Mathematics · #42A61 #47A35 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary: 47D03 #Secondary: 47A30

paper · pdf · doi:10.48550/arxiv.2311.01436

openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give growth estimates for ‖Tⁿ‖ for n→ ∞ in the case T is a strongly Kreiss bounded operator on a UMD Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and L^p-spaces, but also intermediate UMD spaces such as non-commutative L^p-spaces and variable Lebesgue spaces.

Related

• Kreiss bounded and uniformly Kreiss bounded operators
• On the growth rate of powers of a strongly Kreiss bounded operator on L^p-spaces
• Rate of decay of s-numbers
• The UMD constants of the summation operators
• Growth rate of eventually positive Kreiss bounded C₀-semigroups on L^p and C(K)