CLASS OF CSTAR-ALGEBRAS AND TOPOLOGICAL MARKOV-CHAINS
CLASS OF CSTAR-ALGEBRAS AND TOPOLOGICAL MARKOV-CHAINS
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DOI：
10.1007/bf01390048
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发表时间：
1980-01-01
影响因子：
3.1
通讯作者：
KRIEGER, W
中科院分区：
文献类型：
--
作者：
CUNTZ, J;KRIEGER, W
在本文中，我们提出了一类 C* 代数，并指出它与拓扑马尔可夫链的密切关系，拓扑马尔可夫链的理论是符号动力学的一部分。 C* 代数构造从矩阵 A=(A (i, j)) i,~ z, Z 有限集开始，A (i, j) c {0, l}，并且 A 的每一行和每一列都非零。（假设 A (i, j) e {O, 1} 只是为了方便起见。所有构造和结果都扩展到条目为 2~+ 的矩阵。我们在备注 2.18 中对此进行评论。） AC*-代数 6~ A 由部分等距 Si~ O (i~ X) 生成，部分等距作用于希尔伯特空间，使得它们的支持投影 Qi= S* S~ 和它们的范围投影 P~= SIS* 满足关系
In this paper we present a class of C*-algebras and point out its close relationship to topological Markov chains, whose theory is part of symbolic dynamics. The C*-algebra construction starts from a matrix A=(A (i, j)) i,~ z, Z a finite set, A (i, j) c {0, l}, and where every row and every column of A is non-zero.(That A (i, j) e {O, 1} is assumed for convenience only. All constructions and results extend to matrices with entries in 2~+. We comment on this in Remark 2.18.) AC*-algebra 6~ A is then generated by partial isometries Si~ O (i~ X) that act on a Hilbert space in such a way that their support projections Qi= S* S~ and their range projections P~= SIS* satisfy the relations