Abstract
A scattered operator is a bounded linear operator with at most countable spectrum. We prove that if the range of an inner derivation on all bounded linear operators on Hilbert space is contained in the set of scattered operators, then the range is contained in the set of compact operators. As a corollary we prove that on the direct product of countably many copies of B(H), if for some quasinilpotent operator Q, the sum of Q and any quasinilpotent operator is scattered, then Q is compact.
| Original language | English |
|---|---|
| Pages (from-to) | 65-74 |
| Number of pages | 10 |
| Journal | Studia Mathematica |
| Volume | 268 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2023 |
Keywords
- compact operator
- derivation
- scattered element
- scattered radical
- topological radical
Fingerprint
Dive into the research topics of 'Derivations mapping into scattered operators'. Together they form a unique fingerprint.Cite this
Cao, P., & Zhu, S. (2023). Derivations mapping into scattered operators. Studia Mathematica, 268(1), 65-74. https://doi.org/10.4064/sm220205-24-2