Derivations in Commutative C*-Algebras

Abstract

Prof. S. Sakai began the systematic study of unbounded *-derivations in C*-algebras after his work on bounded *-derivations. For the theory of the unbounded *-derivations, he posed many questions in his lecture notes and his talks ([SI, S2]). In the case of commutative C*-algebras, several authors have developed the theory by trying to solve his problems ([Ba], [G]). In consequence, roughly speaking, now we may say that the structure of closed *-derivations has been almost clarified when the underlying space of the commutative C*-algebra is of 0- or 1-dimension, though a few problems have been left unsolved. Furthermore the structure of *-derivations commuting with group actions has rapidly become clear in the last decade. In this note, we shall not mention these structures, using as our references [Bra] and [T].