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Automatic Continuity of Some Types of Double Derivations on Semisimple Banach Algebras | ||
| Journal of Education and Science | ||
| Article 6, Volume 28, Issue 1, 2019, Pages 62-70 PDF (747.02 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/edusj.2019.160913 | ||
| Authors | ||
| Amir A. Mohammed A. Mohammed A. Mohammed; Lamia K. Ismail K. Ismail | ||
| Abstract | ||
| Following Villena in [9] and Mohammed and Ali in [4], we introduce partially defined ( ) - c - double derivation and generalized ( ) - c - double derivation on a semisimple complex Banach algebra whose domain is not necessarily closed, essential ideal and we prove that they are closable. In particular, we show that every ( )- c -double derivation and generalized ( ) - c - double derivation defined on any nonzero ideal of a prime C * - algebra are continuous. | ||
| Keywords | ||
| automatic continuity; double derivation; ultraprimness; sliding hump sequence | ||
| References | ||
|
[1] Johnson B. E. and Sinclair A. M. , “ Continuity of derivations anda
problem of Kaplansky ” , Amer. J. Math. , 90 : 1067 - 1073 (1968) .
[2] Lee T – K . and Liu C – K . , “ Partially defined – derivations on
semisimple Banach algebras” , Studia. Math. , 190 : 193 - 202 (2009).
[3] Mathieu M. , “ Elementary operator on prime C* - algebra ” , Math.
Ann. , 284 : 223 - 244 (1989) .
[4] Mohammed A. A. and Ali S. M. , “ On Villena’s theorem of
automatic continuity of essentially defined derivations on semisimple
Banach algebras ” , Int. J. of Math. Analysis,7 : 2931 - 2939 (2013).
[5] Mahdavian Rad H. and Niknam A. , “ Double derivations, higher
double derivations and automatic continuity ” , J. of sciences, 24 (2) :
165 - 170 (2013) .
[6] Mirzavaziri M. and Moslehian M. S. , “ Automatic continuity of
– derivations on C * - algebras ” , Proc. Amer. Math. Soc. , 134 :
3319 - 3327 (2006) .
[7] Mirzavaziri M. and Omidvar Tehrani E. , “ ( d , ) - double derivations
on C * - algebras ” , Bull. Iranian Math. Soc. , 35 : 147 - 154 (2009).
[8] Parky C. and Yun Shinz D. , “ Generalized ( θ , ø ) - derivations on
Banach algebras ”, Korean J. Math. , 22 (1) : 139 - 150 (2014) .
[9] Villena A. R. , “ Essentially defined derivations on semisimple Banach
algebras ” , Proc. Edinburgh Math. Soc. , 40 : 175 - 179 (1997) .
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