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http://dx.doi.org/10.4134/JKMS.2011.48.4.823

CONTINUITY OF (α,β)-DERIVATIO OF OPERATOR ALGEBRAS  

Hou, Chengjun (Institute of Operations Research Qufu Normal University)
Meng, Qing (School of Mathematical Sciences Qufu Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 823-835 More about this Journal
Abstract
We investigate the continuity of (${\alpha},{\beta}$)-derivations on B(X) or $C^*$-algebras. We give some sufficient conditions on which (${\alpha},{\beta}$)-derivations on B(X) are continuous and show that each (${\alpha},{\beta}$)-derivation from a unital $C^*$-algebra into its a Banach module is continuous when and ${\alpha}$ ${\beta}$ are continuous at zero. As an application, we also study the ultraweak continuity of (${\alpha},{\beta}$)-derivations on von Neumann algebras.
Keywords
automatic continuity; (${\alpha},{\beta}$)-derivation; Banach algebra; algebra; C*-algebra;
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1 R. V. Kadison and J. Ringrose, Fundamentals of the Theory of Operators, Vol 1: Elementary Theory; Vol 2: Advanced Theory, Graduate Studies in Mathematics, Vol. 15, Vol. 16, American Mathematical Society, 1997.
2 I. Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-858.   DOI   ScienceOn
3 I. Kaplansky, Derivation of Banach algebras, Seminar on Analytic Functions, Vol. II. Institute for Advanced Study, Prnceton, 1958.
4 W. S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc. 21 (1969), 695-698.   DOI   ScienceOn
5 M. Mirzavaziri and M. S. Moslehian, Automatic continuity of $\sigma$-derivations on $C^{{\ast}{\ast}}$- algebras, Proc. Amer. Math. Soc. 134 (2006), no. 11, 3319-3327.   DOI   ScienceOn
6 M. Mirzavaziri and M. S. Moslehian, $\sigma$-derivations in Banach algebras, Bull. Iranian Math. Soc. 32 (2006), no. 1, 65-78.
7 M. S. Moslehian, Hyers-Ulam-Rassias stability of generalized derivations, Int. J. Math. Math. Sci. 2006 (2006), Art. ID 93942, 8 pp.
8 J. R. Ringrose, Automatic continuity of derivations of operator algebras, J. London Math. Soc. (2) 5 (1972), 432-438.   DOI
9 S. Sakai, On a conjecture of Kaplansky, Tohoku Math. J. (2) 12 (1960), 31-33.   DOI
10 A. R. Villena, Automatic continuity in associative and nonassociative context, Irish Math. Soc. Bull. No. 46 (2001), 43-76.
11 F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York- Heidelberg, 1973.
12 E. Christensen, Derivations of nest algebras, Math. Ann. 229 (1977), no. 2, 155-161.   DOI
13 H. G. Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs. New Series, 24. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 2000.
14 B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1073.   DOI   ScienceOn
15 R. V. Kadison, Derivations of operator algebras, Ann. of Math. (2) 83 (1966), 280-293.   DOI