Volterra-type inner derivations on Hardy spacesArroussi, 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
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1007/s13398-025-01723-2 Abstract/SummaryA 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.
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