Projections, the Continuous Functional Calculus and C*-Algebras of Real Rank Zero

Details Projections, the Continuous Functional Calculus and C*-Algebras of Real Rank Zero Projections, the Continuous Functional Calculus and C*-Algebras of Real Rank Zero

2012-03-17

arxiv.org/abs/1203.3845v1

Mathematics

Operator Algebras

Scientific paper

We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to C*-algebras of real rank zero, for which we significantly strengthen some fundamental results, specifically on pullbacks of certain operators, excising pure states and Kadison's transitivity theorem. Lastly, we investigate some order properties of the set of projections in C*-algebras of real rank zero.

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