Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 825–828

RIGIDITY OF WEIGHTED COMPOSITION OPERATORS ON H^p

Mikael Lindström, Santeri Miihkinen and Pekka J. Nieminen

Åbo Akademi University, Department of Mathematics
FI-20500 Åbo, Finland; mikael.lindstrom 'at' abo.fi

Åbo Akademi University, Department of Mathematics
FI-20500 Åbo, Finland; santeri.miihkinen 'at' abo.fi

University of Turku, Department of Mathematics and Statistics
FI-20014 University of Turku, Finland; pekka.nieminen 'at' utu.fi

Abstract. We show that every non-compact weighted composition operator f ↦ u · (f ○ φ) acting on a Hardy space H^p for 1 ≤ p < ∞ fixes an isomorphic copy of the sequence space l^p and therefore fails to be strictly singular. We also characterize those weighted composition operators on H^p which fix a copy of the Hilbert space l². These results extend earlier ones obtained for unweighted composition operators.

2010 Mathematics Subject Classification: Primary 47B33, 47B10.

Key words: Hardy space, strict singularity, weighted composition operator.

Reference to this article: M. Lindström, S. Miihkinen and Pekka J. Nieminen: Rigidity of weighted composition operators on H^p. Ann. Acad. Sci. Fenn. Math. 45 (2020), 825–828.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4537

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