Exponential length and exponential rank in C*-algebras
Exponential length and exponential rank in C*-algebras
复制标题
C* 代数中的指数长度和指数等级
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
J. Ringrose
中科院分区：
文献类型：
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作者：
J. Ringrose
在算子代数中，酉群连通分量的一般元可以表示为指数酉元的有限积。最近引入的指数秩的概念是根据为此目的所需的指数的数量来定义的。本文讨论了指数长度的概念，它不是由指数的个数决定，而是由指数的自伴随对数的范数和决定。一个代数的指数长度的知识提供了它的指数秩的上界（但不是相反）。这用于估计算子值连续函数的某些代数的指数秩。
Synopsis In an operator algebra, the general element of the connected component of the unitary group can beexpressed as a finite product of exponential unitary elements. The recently introduced concept of exponential rank is defined in terms of the number of exponentials required for this purpose. The present paper is concerned with a concept of exponential length, determined not by the number of exponentials but by the sum of the norms of their self-adjoint logarithms. Knowledge of the exponential length of an algebra provides an upper bound for its exponential rank (but not conversely). This is used to estimate the exponential rank of certain algebras of operator-valued continuous functions.