Commun. Korean Math. Soc. 1999; 14(1): 157-169
Printed March 1, 1999
Copyright © The Korean Mathematical Society.
Eui-Chai Jeong
Seoul National University
We consider the $C^*$-algebra $O_\infty$ generated by infinite isometries $s_1$, $s_2$, $\cdots$ on Hilbert spaces with the property $\sum_{i=1}^ns_i s_i^*\leqq 1$ for every $n\in \Bbb N$. We present certain type of representations of $C^*$-algebra $O_\infty$ on a separable Hilbert space and study the conditions for irreducibility of these representations.
Keywords: $C^*$-algebra, irreducible representation, decomposition
MSC numbers: Primary 47D30; Secondary 46L45, 47D45, 47S50
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