caa a22 4500 388092238 CHVBK 20180307125255.0 cr unu---uuuuu 161130e199908 xx s 000 0 eng 10.1017/S0004972700033414 doi S0004972700033414 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033414 Topologically simple Banach algebras with derivation [Elektronische Daten] It is not known if a commutative, topologically simple, radical Banach algebra exists. If, however, every derivation on such an algebra is continuous, this yields the automatic continuity of all derivations on commutative, semiprime Banach algebras. Utilising techniques used by Thomas in his proof of the Singer-Wermer conjecture, we show that, if A is a commutative, topologically simple Banach algebra with a non-zero derivation on it, then a quotient of a certain localisation of A has a power series structure. A pivotal role is played by what we call ample sets of denominators. Copyright © Australian Mathematical Society 1999 Illoussamen El Hossein Ecole Normale Supérieure Takaddoum Département de Mathématiques B.P. 5118 10105 Rabat Morocco Runde Volker E-mail: runde@math.uni-sb.de Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 153-161 0004-9727 60:1<153 1999 60 BAZ https://doi.org/10.1017/S0004972700033414 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033414 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Illoussamen El Hossein Ecole Normale Supérieure Takaddoum Département de Mathématiques B.P. 5118 10105 Rabat Morocco NATIONALLICENCE 700 1- Runde Volker E-mail: runde@math.uni-sb.de NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 153-161 0004-9727 60:1<153 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge