Pure and Applied Mathematics Journal
Volume 4, Issue 2, April 2015, Pages: 43-46
Received: Jan. 10, 2015;
Accepted: Jan. 25, 2015;
Published: Feb. 11, 2015
Views 2947 Downloads 195
Youssef Tidli, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Marhaz, Fes, Morroco
Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.
The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra, Pure and Applied Mathematics Journal.
Vol. 4, No. 2,
2015, pp. 43-46.
F.F. Bonsall and J. Duncan, Complete normed algebras, Spring6 Verlag. Berlin (1973).
J. Cusack, Automatic Continuity and topologically simple Banach algebras, J. London. Math. Soc (2), 16 (1977), 439-500.
R. V. Garimella, Continuity of derivation on some semi-prime Banach algebra, Proc. Amer. Math. Soc., 99 (1987), 289 -292.
R.V. Garimella, Prime ideals and the continuity of derivation on integral domins, Indian. J. Pure app. Math, 22 (12) (1991), 1013-1018.
R.V. Garimella, On nilpotenty of the separting ideal of a derivation. Proc. Amer. Math. Soc., 117, (1993), 167-174.
N. Jacobson, Basic Algebra II, W. H. Ferman and Compagny (1980).
B.E Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73, (1967) 537-539
B.E Johnson, and A. M. Sinclair, Continuity of derivation and a problem of Kaplansky, Amer. J. Math. Math. 90 (1968), 1067-1073.
M. Mathieu et V. Runde, Derivations mapping into the radical II, Bull. London Math. Soc., 24(1992), 485-487.
V. Runde, Continuity of derivations and epimorphisms, Pacific J. of Math., Vol. 147, Nr. 2 (1991), 365-374.
A. M. Sinclair, Automatic Continuity of linear operators, London. Math. Soc. Lecture Note Series 21 (C.U.P., Combridge 1976).
Y. TIDLI, L. OUKHTITE, A. TAJMOUATI, On the Automatic continuity of the epimorphisms in *algebras of Banach. IJMMS 2004: 22 1183-1187 (2002).