Author:
Deng Chenxi,Lorist Emiel,Veraar Mark
Abstract
AbstractIn this paper we give growth estimates for $$\Vert T^n\Vert $$
‖
T
n
‖
for $$n\rightarrow \infty $$
n
→
∞
in the case T is a strongly Kreiss bounded operator on a $${{\,\textrm{UMD}\,}}$$
UMD
Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and $$L^p$$
L
p
-spaces, but also intermediate $${{\,\textrm{UMD}\,}}$$
UMD
spaces such as non-commutative $$L^p$$
L
p
-spaces and variable Lebesgue spaces.
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Arnold, L., Cuny, C.: Strongly Kreiss bounded operators on $$L^p$$ spaces. arXiv:2302.14135 (2023)
2. Bonilla, A., Müller, V.: Kreiss bounded and uniformly Kreiss bounded operators. Rev. Mat. Complut. 34(2), 469–487 (2021)
3. Bourgain, J.: On trigonometric series in super reflexive spaces. J. Lond. Math. Soc. Ser. 2, 24(1), 165–174 (1981)
4. Bourgain, J.: Vector-valued singular integrals and the $$H^1$$-BMO duality. In: Chao, J.-A., Woyczynski, W.A. (Eds.) Probability Theory and Harmonic Analysis (Cleveland, Ohio, 1983), Monographs and Textbooks in Pure and Applied Mathematics, vol. 98, pp. 1–19. Dekker, New York (1986)
5. Calderón, A.-P.: Intermediate spaces and interpolation, the complex method. Stud. Math. 24, 113–190 (1964)