拟 *-代数中表示的扩张
Extension of representations in quasi *-algebras
摘要：
设$(A, A_o)$是拓扑拟 *-代数，这特别意味着$A_o$是拓扑 *-代数，在$A$中稠密.设$π^o$是$A_o$在某个pre-Hilbert空间${\cal D} \subset {\cal H}$中的 *-表示.然后，我们给出了几种将$π^o$通过闭包推广到包含在$A$中的更大的拟 *-代数的方法，无论是通过Hilbert空间算子，还是通过${\cal D}$上的半双线性形式.明确的例子进行了讨论，交换和nonabel，包括CCR代数。
英文摘要：
Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $π^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\cal D} \subset {\cal H}$. Then we present several ways of extending $π^o$, 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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