Compactification, and beyond, of composition operators on Hardy spaces by weights

Daniel Li (1) , Hervé Queffélec (2) , Luis Rodriguez-Piazza (3) , Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens
2 LPP - Laboratoire Paul Painlevé
3 Departamento de Analisis Matematico

We study when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can turn a compact composition operator into a non-compact one. MSC 2010 primary: 47B33 ; secondary: 46B28

Keywords: Key-words approximation numbers; composition operator; compactification; decompactification; Hilbert-Schmidt operator; p-summing operators; Schatten classes

Domains: Mathematics [math]; Functional Analysis [math.FA]

Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza, Pascal Lefèvre. Compactification, and beyond, of composition operators on Hardy spaces by weights. 2019. ⟨hal-02097606⟩