A1 Refereed original research article in a scientific journal
Rigidity of weighted composition operators on H-p
Authors: Mikael Lindström, Santeri Miihkinen, Pekka J. Nieminen
Publisher: SUOMALAINEN TIEDEAKATEMIA
Publication year: 2020
Journal: Annales Academiae Scientiarum Fennicae. Mathematica
Journal name in source: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Journal acronym: ANN ACAD SCI FENN-M
Volume: 45
First page : 825
Last page: 828
Number of pages: 4
ISSN: 1239-629X
DOI: https://doi.org/10.5186/aasfm.2020.4537
Web address : http://www.acadsci.fi/mathematica/Vol45/LindstromMiihkinenNieminen.html
Abstract
We show that every non-compact weighted composition operator f bar right arrow u . (f omicron phi) acting on a Hardy space H-p for 1 <= p < infinity fixes an isomorphic copy of the sequence space lp and therefore fails to be strictly singular. We also characterize those weighted composition operators on Hp which fix a copy of the Hilbert space l(2). These results extend earlier ones obtained for unweighted composition operators.
We show that every non-compact weighted composition operator f bar right arrow u . (f omicron phi) acting on a Hardy space H-p for 1 <= p < infinity fixes an isomorphic copy of the sequence space lp and therefore fails to be strictly singular. We also characterize those weighted composition operators on Hp which fix a copy of the Hilbert space l(2). These results extend earlier ones obtained for unweighted composition operators.
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