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Extension of representations in quasi *-algebras

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 نشر من قبل Fabio Bagarello
 تاريخ النشر 2009
  مجال البحث فيزياء
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Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${cal D} subset {cal H}$. Then we present several ways of extending $pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.


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