Journal article
Circle companions of Hardy spaces of the unit disk
Journal of functional analysis, Vol.285(12), 110159
12/15/2023
DOI: 10.1016/j.jfa.2023.110159
Abstract
This paper gives a complete answer to the following problem: Find the circle companion of the Hardy space of the unit disk with values in the space of all bounded linear operators between two separable Hilbert spaces. Classically, the problem asks whether for each function h on the unit disk, there exists a “boundary function” bh on the unit circle such that the mapping
is an isometric isomorphism between Hardy spaces of the unit circle and the unit disk with values in some Banach space. For the case of bounded linear operator-valued functions, we construct a Hardy space of the unit circle such that its elements are SOT measurable, and their norms are integrable: indeed, this new space is isometrically isomorphic to the Hardy space of the unit disk via a “strong Poisson integral.”
Details
- Title: Subtitle
- Circle companions of Hardy spaces of the unit disk
- Creators
- Raúl E. Curto - University of IowaIn Sung Hwang - Sungkyunkwan UniversitySumin Kim - Sungkyunkwan UniversityWoo Young Lee - Seoul National University
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.285(12), 110159
- DOI
- 10.1016/j.jfa.2023.110159
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Grant note
- DOI: 10.13039/100003187, name: NSF; DOI: 10.13039/501100003725, name: National Research Foundation of Korea, award: 2020R1I1A1A01053085, 2021R1A2C1005428, 2022R1A2C1010830; DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-2247167
- Language
- English
- Electronic publication date
- 09/2023
- Date published
- 12/15/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984463078102771
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