Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.

Abstract

In this article, the notion of $n-$derivation is introduced for all integers $n\geq 2$. Although all derivations are $n-$derivations,  in general these notions are not equivalent. Some properties of ordinary derivations are  investigated for $n-$derivations. Also, we show that under certain mild condition  $n-$derivations are derivations.

Keywords

Main Subjects

[1] F. F. Bonsall and J. Duncan, Complete normed algebras, Springpr-Verlag, New York, 1973.
[2] G. Dales, Banach Algebra and Automatic Continuity, London Mathematical Society Monographs, Volume 24, Clarendon Press, Oxford, 2000.
[3] H. G. Dales, F. Ghahramani, and N. Gronbaek, Derivations into iterated duals of Banach algebras, Studia Math., 128 (1998), 19-54.
[4] N. Dunford and J. T. Schwartz, Linear operators, Part I, New York, Interscience, 1958.
[5] F. Ghahramani, Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc., 21 (1980), 149-161.
[6] M. Hejazian, M. Mirzavaziri, and M. S. Moslehian, n-Homomorphism, Bull. Iranian Math. Soc., 31(1) (2005), 13-23.
[7] B. E. Johnson, Local derivations on C* algebras are derivations, Trans. Amer. Math. Soc., 353 (2000), 313-325.
[8] I. Kaplansky, Derivations of Banach algebras, In Seminars on analytic functions, Vol. 2, Princeton Univ. Press, Princeton, 1958.
[9] E. Samei, Approximately local derivations, J. London Math. Soc., 71(2) (2005), 759-778.
[10] A. M. Sinclair, Continuous derivations on Banach algebras , Proc. Amer. Math. Soc., 20 (1969), 166-170.
[11] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann., 129 (1955) 260-264.
[12] S. Watanabe, A Banach algebra which is an ideal in the second dual space, Sci. Rep. Niigata Univ. Ser., A 11 (1974), 95-101.