Volterra-type inner derivations on Hardy spaces

Arroussi, H., Tong, C., Virtanen, J. A. and Yuan, Z. (2025) Volterra-type inner derivations on Hardy spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 119 (2). ISSN 1579-1505 doi: 10.1007/s13398-025-01723-2

Abstract/Summary

A classical result of Calkin [Ann. of Math. (2) 42 (1941), pp. 839–873] says that an inner derivation maps the algebra of bounded operators on a Hilbert space into the ideal of compact operators if and only if T is a compact perturbation of the multiplication by a scalar. In general, an analogous statement fails for operators on Banach spaces. To complement Calkin’s result, we characterize Volterra-type inner derivations on Hardy spaces using generalized area operators and compact intertwining relations for Volterra and composition operators. Further, we characterize the compact intertwining relations for multiplication and composition operators between Hardy and Bergman spaces.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/122078
Identification Number/DOI	10.1007/s13398-025-01723-2
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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