Über die Struktur maximaler Ideale in LMC*-Algebren

Abstract

We describe the structure of dense maximal left ideals for the simplest non-commutative LMC*-algebras. Further we show, for these examples, that the correspondence "dense maximal left ideals $\to$ extremal states of the bounded part of the algebra, not extendable to continuous states of the whole algebra" is not one-to-one as in the commutative case.