Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 601-613
Adam Mickiewicz
University Poznan,
Faculty of Mathematics and Computer Science
Umultowska 87, 61-614 Poznan, Poland;
mastylo 'at' amu.edu.pl
Adam Mickiewicz
University Poznan,
Faculty of Mathematics and Computer Science
Umultowska 87, 61-614 Poznan, Poland; pml 'at' amu.edu.pl
Abstract. In the paper composition operators acting on quasi-Banach spaces of analytic functions on the unit disc of the complex plane are studied. In particular characterizations in terms of a function φ of order bounded as well as summing operators Cφ are presented, if Cφ is an operator from an abstract Hardy space. Applications are shown for the special case of Hardy–Orlicz, Hardy–Lorentz, and growth spaces.
2010 Mathematics Subject Classification: Primary 47B33, 47B38; Secondary 47B10.
Key words: Hardy space, interpolation space, composition operators, absolutely summing operators, growth spaces, order bounded operators.
Reference to this article: M. Mastylo and P. Mleczko: Composition operators on Banach spaces of analytic functions. Ann. Acad. Sci. Fenn. Math. 44 (2019), 601-613.
https://doi.org/10.5186/aasfm.2019.4436
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