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

DOI:
https://doi.org/10.1090/S0002-9939-00-05890-1

Published electronically:
June 21, 2000

MathSciNet review:
1777581

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Abstract | References | Similar Articles | Additional Information

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 , , where is the algebra of all bounded Hilbert space operators, and , , , are normal operators, such that , and . 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:
https://doi.org/10.1090/S0002-9939-00-05890-1

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