Proceedings of the American Mathematical Society

Une remarque sur l'orthogonalité de l'image au noyau d'une dérivation généralisée

Author(s): M. Benlarbi Delai; S. Bouali; S. Cherki
Journal: Proc. Amer. Math. Soc. 126 (1998), 167-171.
MSC (1991): Primary 47B47, 47A30, 47B20; Secondary 47B10
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract: In this paper we introduce the notion of the pair $(A,B)$

of operators having the Fuglede-Putnam property in a two-sided ideal of $L(H)$

. The characterization of this class allows us to generalize the recent result of F. Kittaneh. We also give some applications of this result.

1.: Anderson, J. H., On normal derivations, Proc. Amer. Math Soc. 38 (1973), 135-140. MR 47:875
2.: Bouali, S. & Charles, J., Extention de la notion d'opérateur -symétrique, I, Acta Sci. Math. 58 (1993), 517-525. MR 95e:47048
3.: Bouali, S. & Charles, J., Extention de la notion d'opérateur -symétrique II, Linear Algebra and its Applications 225: (1995), 175-185.
4.: Bouali, S. & Cherki, S., Approximation by Generalized Commutators, Acta. Sci. Math. 63 (1997), 15-20.
5.: Duggal, B. P., A remark on normal derivations of Hilbert-Schmidt Type, Monatsh. Math. 112: (1991), 265-270. MR 92m:47067
6.: Fuglede, B., A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. 36 (1950), 35-40. MR 11:371c
7.: Gohberg & Krein, M. G., Introduction to the theory of linear nonselfadjoint operators, Transl. Math. monographs 18A (1969). MR 39:7447
8.: Kittaneh, F., On the commutants modulo of and , J. Austral. Math. 41 (1986), 47-50. MR 87k:47047
9.: Kittaneh, F., Normal derivations in Hilbert-Schmidt type, Glasgow Math. J. 29 (1987), 245-248. MR 88k:47049
10.: Kittaneh, F., Normal derivations in norm ideals, Proc. Amer. Math. Soc. 123: n6 (1995), 1779-1785. MR 95g:47054
11.: Maher, P. J., Commutator approximants, Proc. Amer. Math. Soc. Vol. 115: n 4 (1992), 995-1000. MR 92j:47059
12.: Takahashi, K., On the converse of the Fuglede-Putnam Theorem, Acta. Sci. Math. 43: (1981), 123-125. MR 82g:47018
13.: Tong, Y., Kernels of generalized derivations, Acta Sci. Math. 54 1-2 (1990), 159-169. MR 92f:47032
14.: Yoshino, T., Subnormal operator with a cyclic vector, Tohoku Math. J. 21: (1969), 47-55. MR 39:7450
15.: Yoshino, T., Remark on the generalized Putnam-Fuglede Theorem, Proc. Amer. Math. Soc. 95 n 4: (1985), 571-572. MR 87i:47034

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B47, 47A30, 47B20, 47B10

M. Benlarbi Delai
Affiliation: Université II, Place Eugène Bataillon, Département de Mathématiques, 34095 Montpellier Cedex 5, France - Faculté des Sciences, Mohammed V, Département de Mathématiques et d'Informatique, Rabat, Morocco

S. Bouali
Affiliation: Faculté des Sciences, Ibn Tofail, Département de Mathématiques et d'Informatique, Kenitra, Morocco

S. Cherki
Affiliation: Faculté des Sciences et Techniques, Département de Mathématiques, Tanger, Maroc

DOI: 10.1090/S0002-9939-98-03996-3
PII: S 0002-9939(98)03996-3
Keywords: Generalized derivation, Fuglede-Putnam Theorems, norm ideal, orthogonality result for derivations, suites noyaux
Received by editor(s): June 26, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS