On Stability of C-algebras
On Stability of C-algebras
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关于 C 代数的稳定性
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
M. Rørdam
中科院分区：
文献类型：
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作者：
J. Hjelmborg;M. Rørdam
设a是一个-单位代数，即a允许一个可数的近似单位。这被证明是稳定的,即同构创设toA K whereK紧算子的代数是可分离的希尔伯特空间,当且仅当每个正elementa 2 a和每一个“2 > 0存在积极的元素b thatkabk <“andx x = a, xx somex = b的a .使用这个特性是在其他方面证明了任何序列的归纳极限-unital stableC代数是稳定的,一个-单位稳定代数与一个离散群的叉乘也是稳定的。
LetA be a -unitalC -algebra, i.e.A admits a countable approximate unit. It is proved thatA is stable, i.e.A is isomorphic toA K whereK is the algebra of compact operators on a separable Hilbert space, if and only if for each positive elementa 2 A and each" > 0 there exists a positive element b 2 A such thatkabk < " andx x = a, xx = b for somex in A. Using this characterization it is proved among other things that the inductive limit of any sequence of -unital stableC -algebras is stable, and that the crossed product of a -unital stableC -algebra by a discrete group is again stable.