局部凸拟$C^*$ -代数的结构
Structure of locally convex quasi $C^*$-algebras
摘要：
（赋范）$C^*$ -代数$A_0[\| \cdot \|_0]$关于$A_0$上的局部凸拓扑$τ$的完备化使得$A_0$的乘法分别连续，一般来说，它是拟 *-代数，而不是局部凸 *-代数.在这种方式下，导致考虑局部凸的准$C^*$ -代数，它推广了$C^*$ -代数的背景下，准 *-代数。给出了例子，并研究了$C^*$ -代数的这些亲戚的结构.
英文摘要：
The completion of a (normed) $C^*$-algebra $A_0[\| \cdot \|_0]$ with respect to a locally convex topology $τ$ on $A_0$ that makes the multiplication of $A_0$ separately continuous is, in general, a quasi *-algebra, and not a locally convex *-algebra. In this way, one is led to consideration of locally convex quasi $C^*$-algebras, which generalize $C^*$-algebras in the context of quasi *-algebras. Examples are given and the structure of these relatives of $C^*$-algebras is investigated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
