Let $(\A, \A_o)$ be a topological \qxa, which means in particular that $\A_o$ is a topological \xa, dense in \A. Let $\pi^o$ be a *-representation of $\A_o$ in some pre-Hilbert space $\D \subset \H$. Then we present several ways of extending $\pi^o$, by closure, to some larger \qxa\ contained in \A, either by Hilbert space operators, or by sesquilinear forms on \D. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.

Antoine, J., Bagarello, F., Trapani, C. (1998). Extension of representations in quasi *-algebras. ANNALES DE L'INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE, 69(6), 241-264.

Extension of representations in quasi *-algebras

BAGARELLO, Fabio;TRAPANI, Camillo
1998-01-01

Abstract

Let $(\A, \A_o)$ be a topological \qxa, which means in particular that $\A_o$ is a topological \xa, dense in \A. Let $\pi^o$ be a *-representation of $\A_o$ in some pre-Hilbert space $\D \subset \H$. Then we present several ways of extending $\pi^o$, by closure, to some larger \qxa\ contained in \A, either by Hilbert space operators, or by sesquilinear forms on \D. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.
1998
Antoine, J., Bagarello, F., Trapani, C. (1998). Extension of representations in quasi *-algebras. ANNALES DE L'INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE, 69(6), 241-264.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/198942
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