A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Derivations mapping into scattered operators

Volume 268 / 2023

Peng Cao, Sen Zhu Studia Mathematica 268 (2023), 65-74 MSC: Primary 47B07; Secondary 47B47, 47B48, 46H20. DOI: 10.4064/sm220205-24-2 Published online: 6 July 2022

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 $\textbf B(\mathcal H)$, if for some quasinilpotent operator $Q$, the sum of $Q$ and any quasinilpotent operator is scattered, then $Q$ is compact.

Authors

  • Peng CaoSchool of Mathematics and Statistics
    Beijing Institute of Technology
    Beijing, 102488, P.R. China
    and
    Beijing Key Laboratory
    on Mathematical Characterization Analysis
    and Applications of Complex Information
    Beijing Institute of Technology
    Beijing 102488, P.R. China
    e-mail
  • Sen ZhuDepartment of Mathematics
    Jilin University
    Changchun 130012, P.R. China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image