## Orthogonality of the range and the kernel of some elementary operators

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- by Dragoljub Kečkić PDF
- Proc. Amer. Math. Soc.
**128**(2000), 3369-3377 Request permission

## Abstract:

We prove the orthogonality of the range and the kernel of an important class of elementary operators with respect to the unitarily invariant norms associated with norm ideals of operators. This class consists of those mappings $E:B(H)\to B(H)$, $E(X)=AXB+CXD$, where $B(H)$ is the algebra of all bounded Hilbert space operators, and $A$, $B$, $C$, $D$ are normal operators, such that $AC=CA$, $BD=DB$ and $\ker A\cap \ker C=\ker B\cap \ker D=\{0\}$. Also we establish that this class is, in a certain sense, the widest class for which such an orthogonality result is valid. Some other related results are also given.## References

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## Additional Information

**Dragoljub Kečkić**- Affiliation: Matematički fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia
- Email: keckic@matf.bg.ac.yu
- Received by editor(s): February 20, 1998
- Received by editor(s) in revised form: January 17, 1999
- Published electronically: June 21, 2000
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**128**(2000), 3369-3377 - MSC (2000): Primary 47B10, 47B47, 47L20; Secondary 46B20, 47A30
- DOI: https://doi.org/10.1090/S0002-9939-00-05890-1
- MathSciNet review: 1777581