Derivations on Real and Complex JB*-Triples |
| |
Authors: | Ho, Tony Martinez-Moreno, Juan Peralta, Antonio M. Russo, Bernard |
| |
Affiliation: | Department of Mathematics, University of California Irvine, CA 92697-3875, USA Department of Mathematics, University of California Irvine, CA 92697-3875, USA, brusso{at}math.uci.edu Departamento Análisis Matemático, Facultad de Ciencias, Universidad de Granada 18071 Granada, Spain, jmmoreno{at}goliat.ugr.es Departamento Análisis Matemático, Facultad de Ciencias, Universidad de Granada 18071 Granada, Spain, aperalta{at}goliat.ugr.es |
| |
Abstract: | At the regional conference held at the University of California,Irvine, in 1985 [24], Harald Upmeier posed three basic questionsregarding derivations on JB*-triples: (1) Are derivations automatically bounded? (2) When are all bounded derivations inner? (3) Can bounded derivations be approximated by inner derivations? These three questions had all been answered in the binary cases.Question 1 was answered affirmatively by Sakai [17] for C*-algebrasand by Upmeier [23] for JB-algebras. Question 2 was answeredby Sakai [18] and Kadison [12] for von Neumann algebras andby Upmeier [23] for JW-algebras. Question 3 was answered byUpmeier [23] for JB-algebras, and it follows trivially fromthe KadisonSakai answer to question 2 in the case ofC*-algebras. In the ternary case, both question 1 and question 3 were answeredby Barton and Friedman in [3] for complex JB*-triples. In thispaper, we consider question 2 for real and complex JBW*-triplesand question 1 and question 3 for real JB*-triples. A real orcomplex JB*-triple is said to have the inner derivation propertyif every derivation on it is inner. By pure algebra, every finite-dimensionalJB*-triple has the inner derivation property. Our main results,Theorems 2, 3 and 4 and Corollaries 2 and 3 determine whichof the infinite-dimensional real or complex Cartan factors havethe inner derivation property. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|