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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Orthogonality of the range and the kernel of some elementary operators


Author: Dragoljub Keckic
Journal: Proc. Amer. Math. Soc. 128 (2000), 3369-3377
MSC (2000): Primary 47B10, 47B47, 47L20; Secondary 46B20, 47A30
Published electronically: June 21, 2000
MathSciNet review: 1777581
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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.


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Additional Information

Dragoljub Keckic
Affiliation: Matematički fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia
Email: keckic@matf.bg.ac.yu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05890-1
PII: S 0002-9939(00)05890-1
Keywords: Orthogonality of subspaces, unitarily invariant norms, normal operator, elementary operators
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
Article copyright: © Copyright 2000 American Mathematical Society