DECOMPOSITION OF STAR-HOMOMORPHISMS OF UNBOUNDED OPERATOR-ALGEBRAS

We shall introduce a class of unbounded operator algebras called regular O*-algebras which is a wider class than EW*-algebras and closed O*-algebras satisfying condition (I), and show that every *-homomorphism-PHI of a closed O*-algebra M onto a regular O*-algebra N with a regular basis {eta(lambda))lambda-epsilon-LAMBDA such that omega-eta-lambda-degrees-PHI is a sigma-vector form on M for each lambda-epsilon-LAMBDA is composed of an ampliation, an induction and a spatial isomorphism. This is an extension of the results of Inoue 5 and Bhatt 2.