Infinite norm decompositions of C${}^{\ast }$-algebras

Abstract

In the given article the notion of infinite norm decomposition of a C${}^{\ast }$-algebra is investigated. The norm decomposition is some generalization of Peirce decomposition. It is proved that the infinite norm decomposition of any C${}^{\ast }$-algebra is a C${}^{\ast }$-algebra. C${}^{\ast }$-factors with an infinite and a nonzero finite projection and simple purely infinite C${}^{\ast }$-algebras are constructed.