Strongly Kreiss bounded operators in UMD Banach spaces

Chenxi Deng; Emiel Lorist

doi:10.1007/s00233-024-10441-x

Strongly Kreiss bounded operators in UMD Banach spaces

Chenxi Deng, Emiel Lorist^*

^*Corresponding author for this work

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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.

Original language	English
Pages (from-to)	594-625
Number of pages	32
Journal	Semigroup Forum
Volume	108
Issue number	3
DOIs	https://doi.org/10.1007/s00233-024-10441-x
Publication status	Published - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

(Strongly) Kreiss bounded
Decompositions
Discrete semigroup
Fourier multipliers
Power boundedness
UMD space

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AU - Lorist, Emiel

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N2 - 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 Lp-spaces, but also intermediate UMD spaces such as non-commutative Lp-spaces and variable Lebesgue spaces.

AB - 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 Lp-spaces, but also intermediate UMD spaces such as non-commutative Lp-spaces and variable Lebesgue spaces.

KW - (Strongly) Kreiss bounded

KW - Decompositions

KW - Discrete semigroup

KW - Fourier multipliers

KW - Power boundedness

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VL - 108

SP - 594

EP - 625

JO - Semigroup Forum

JF - Semigroup Forum

IS - 3

ER -

Strongly Kreiss bounded operators in UMD Banach spaces

Abstract

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Keywords

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