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[en] We first give a quick survey of the realization of symmetries of quantum systems in the various formalisms of quantum mechanics: traditional (Hilbert space), algebraic (C*-algebras), rigged Hilbert spaces, *-algebras of unbounded operators, partial *-algebras of closable operators. Then we describe in some detail the concept of partial inner product spaces (PIP-spaces) and operators on them. Finally, we examine various classes of operators on PIP-spaces that allow a correct realization of symmetries
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121; 
; v. 41(30); [13 p.]
; v. 41(30); [13 p.]