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- Publisher
- Springer Journals
- Copyright
- Copyright © Tusi Mathematical Research Group (TMRG) 2021
- ISSN
- 2639-7390
- eISSN
- 2008-8752
- DOI
- 10.1007/s43034-021-00151-8
- Publisher site
- See Article on Publisher Site
Abstract
Let Fαp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_\alpha ^p$$\end{document} be the weighted Fock space in Cn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {C}^{n}$$\end{document} with α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document} real and 0<p≤∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0<p\le \infty$$\end{document}. In this paper, we completely characterize the topological components and isolated elements of the set of bounded composition operators acting on Fαp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_\alpha ^p$$\end{document} in the uniform operator topology. Meanwhile, we show that Gleason’s problem on Fαp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_\alpha ^p$$\end{document} in Cn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {C}^{n}$$\end{document} is solvable.
Journal
Annals of Functional Analysis – Springer Journals
Published: Jan 1, 2022
Keywords: Weighted Fock space; Composition operator; Gleason’s problem; Topological component; 30H20; 47B33