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Non-normal derivation and orthogonality
Author(s):
Salah
Mecheri
Journal:
Proc. Amer. Math. Soc.
133
(2005),
759-762.
MSC (2000):
Primary 47B47, 47A30, 47B20;
Secondary 47B10
Posted:
October 7, 2004
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Abstract:
The main purpose of this note is to characterize the operators which are orthogonal (in the sense of James) to the range of a generalized derivation for non-normal operators
References:
-
- 1.
- J. Anderson, On normal derivations, Proc. Amer. Math. Soc. 38-1(1973), 135-140. MR 47:875
- 2.
- B.P. Duggal, A remark on normal derivations, Proc. Amer. Math. Soc. 126-7(1998), 2047-2052. MR 98h:47050
- 3.
- F. Kittaneh, Operators that are orthogonal to the range of a derivation, J. Math. Anal. Appl. 203(1996), 863-873. MR 97f:47033
- 4.
- F.Kittaneh, Normal derivations in norm ideals, Proc. Amer. Math. Soc., 123-6(1995)1779-1785. MR 95g:47054
- 5.
- P.J. Maher, Commutator approximants, Proc. Amer. Math. Soc. 115(1992), 995-1000. MR 92j:47059
- 6.
- S. Mecheri, On minimizing
Serdica Math. J. 26 (2000), no. 2, 119-126. MR 2001j:47033 - 7.
- S. Mecheri, On the orthogonality in von Neumann-Shatten classes, Int. Jour. Appl. Math, 8(2002), 441-447. MR 2003b:47063
- 8.
- S. Mecheri and A.Bachir, Generalized derivation modulo the ideal of all compact operators, Int.Jour.Math.Math.Sc., 32.8(2002), 501-506. MR 2003i:47038
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Additional Information:
Salah
Mecheri
Affiliation:
Department of Mathematics, King Saud University College of Science, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Email:
mecherisalah@hotmail.com
DOI:
10.1090/S0002-9939-04-07609-9
PII:
S 0002-9939(04)07609-9
Keywords:
Derivation,
generalized derivation,
orthogonality
Received by editor(s):
February 11, 2003
Received by editor(s) in revised form:
October 16, 2003
Posted:
October 7, 2004
Additional Notes:
This work was supported by the Research Center Project No. {\bf Math/1422/10}
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2004,
American Mathematical Society
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