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Representations and derivations of quasi \(*\)-algebras induced by local modifications of states. (English) Zbl 1170.46048

Summary: The relationship between the GNS representations associated to states on a quasi \(*\)-algebra which are local modifications of each other (in a sense which we will discuss) is examined. The role of local modifications on the spatiality of the corresponding induced derivations describing the dynamics of a given quantum system with infinite degrees of freedom is discussed.

MSC:

46K10 Representations of topological algebras with involution
47L60 Algebras of unbounded operators; partial algebras of operators
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