Journal of the Ramanujan Mathematical Society

Chunlan Jiang ¹, Rui Shi ¹

Affiliations
1 Mathematics and Information Science College, Hebei Normal University, Shijiazhuang-050016, CN

Abstract

Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written as direct sums of at most countably many strongly irreducible operators. In this paper, we show that a bounded linear operator A is similar to a direct integral of strongly irreducible operators if its commutant {A}' contains a bounded maximal abelian set of idempotents. We find that bounded linear operators which are similar to direct integrals of strongly irreducible operators form a dense subset of ℒ(ℋ) in the operator norm.

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Chunlan Jiang ¹, Kun Wang ²

Affiliations
1 College of Mathematics Hebei Normal University Shijiazhuang, 050016, Hebei, CN
2 Department of Mathematics, University of Puerto Rico, Rio Piedras Campus, P.O.Box 70377, San Juan, Puerto Rico, US

Abstract

Let A = lim (An, φn,m) be an inductive limit C∗-algebra with An = ⨁kni =1 Ai n with the Ai n splitting interval algebras. Suppose that A has the ideal property: each closed two-sided ideal is generated (as an ideal) by projections in the ideal. In this article, we will show that the scaled ordered K0 group and the ordered vector spaces AffT(eAe) with e a projection together with the natural maps between them are complete invariants for the classification of this class of C∗-algebras.

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