EXTENSIONS OF FACTORIAL STATES OF CSTAR-ALGEBRAS

Let A be a C*-algebra, B be a C*-subalgebra of A, and φ be a factorial state of B. Sometimes, φ may be extended to a factorial state of A by a tensor product method of Sakai ("C*-algebras and W*-algebras, Springer-Verlag, Berlin/Heidelberg/ New York 1971"). Sometimes, there is a weak expectation of A into πφ(B), and then factorial extensions may be found by a method of Sakai and Tsui (Yokohama Math. J.29 (1981), 157-160). These two methods are shown to have the same effect, and the factorial extensions produced by them are analysed. © 1985