Riesz decomposition in inductive limit \(C^*\)-algebras. (English) Zbl 0820.46064

Goodearl, Kenneth R.

Rocky Mt. J. Math. 24, No. 4, 1405-1430 (1994).

Summary: As recently proved by Zhang, the projections in any \(C^*\)-algebra of real rank zero enjoy the Riesz decomposition property. Here the Riesz decomposition property is obtained for projections in several types of \(C^*\)-algebras with positive real rank, including the inductive limits with slow dimension growth introduced by Blackadar, Dǎdǎrlat, and Rørdam. Waiving the dimension restrictions, weaker forms of the Riesz decomposition property are established for general inductive limits of finite direct products of homogeneous \(C^*\)-algebras.

MSC:

46L80	\(K\)-theory and operator algebras (including cyclic theory)
46M40	Inductive and projective limits in functional analysis
19K14	\(K_0\) as an ordered group, traces

Keywords:

projections; real rank zero; Riesz decomposition property; inductive limits of finite direct products of homogeneous \(C^*\)-algebras

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