Geodesic
Compactification, and beyond, of composition operators on Hardy spaces by weights
Pascal Lefèvre1 ; Daniel Li1 ; Hervé Queffélec2 ; Luis Rodríguez-Piazza3
1 Université d'Artois, Laboratoire de Mathématiques de Lens (LML) UR 2462 & Fédération Mathématique des Hauts-de-France FR 2037 CNRS
2 Université Lille Nord de France, USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524 & Fédération Mathématique des Hauts-de-France FR 2037 CNRS
3 Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 43-57

Voir la notice de l'article provenant de la source Journal.fi

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.
Keywords: Approximation numbers, composition operator, compactification, decompactification, Hilbert-Schmidt operator, p-summing operators, Schatten classes

Pascal Lefèvre 1 ; Daniel Li 1 ; Hervé Queffélec 2 ; Luis Rodríguez-Piazza 3

1 Université d'Artois, Laboratoire de Mathématiques de Lens (LML) UR 2462 & Fédération Mathématique des Hauts-de-France FR 2037 CNRS
2 Université Lille Nord de France, USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524 & Fédération Mathématique des Hauts-de-France FR 2037 CNRS
3 Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático 
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Pascal Lefèvre; Daniel Li; Hervé Queffélec; Luis Rodríguez-Piazza. Compactification, and beyond, of composition operators on Hardy spaces by weights. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 43-57. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a2/