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Cyclic generalized vectors for algebras of unbounded operators. (English) Zbl 0836.47036

Unbounded operator algebras in Hilbert space are generalizations of observable algebras known in quantum mechanics. Technical difficulties with their representations are related to the existence of cyclic vectors.
The authors consider a class of unbounded operator algebras in Hilbert space, which allow the existence of such a vector. Motivation for this work can be traced back to generalized vectors theory, weights on \(O^*\) algebras, and extended Tomita-Takesaki theory.

MSC:

47L60 Algebras of unbounded operators; partial algebras of operators
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