Differences of composition operators on the Bloch spaces. (English) Zbl 1174.47019

The topics of the paper are the boundedness and the compactness in the Bloch spaces (big and small) of the difference of two composition operators. The motivations, well explained in the second page, is the closeness of these questions to a relevant result of J. H. Shapiro and C. Sundberg [Pac. J. Math. 145, No. 1, 117–152 (1990; Zbl 0732.30027)]. In the second section, the basic inequalities are recalled. In Section 3, boundedness and compactness of the difference of two composition operators are carefully characterized; in particular, it is proved that weak compactness of the difference on the little Bloch space together with continuity is equivalent to compactness. In the final section, a problem of the topological structure of the composition operators in the space of operators is addressed.


47B33 Linear composition operators


Zbl 0732.30027