Volterra and composition inner derivations on the Fock–Sobolev spaces

Yang, X., He, H., Tong, C. and Arroussi, H. (2024) Volterra and composition inner derivations on the Fock–Sobolev spaces. Complex Analysis and Operator Theory, 18 (5). 103. ISSN 1661-8262 doi: 10.1007/s11785-024-01537-x

Abstract/Summary

On the Fock–Sobolev spaces, we study the range of Volterra inner derivations and composition inner derivations. The Volterra inner derivation ranges in the ideal of compact operators if and only if the induced function g is a linear polynomial. The composition inner derivation ranges in the ideal of compact operators if and only if the induced function is either identity or a contractive linear self-mapping of . Moreover, we describe the compact intertwining relations for composition operators and Volterra operators between different Fock–Sobolev spaces. In this paper, our results are complement and in a sense extend some aspects of Calkin’s result (Ann Math 42:839–873, 1941) to the algebras of bounded linear operators on Fock–Sobolev spaces.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/119613
Identification Number/DOI	10.1007/s11785-024-01537-x
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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