Cuntz semigroups of C*-algebras of stable rank one and projective Hilbert modules

Details Cuntz semigroups of C*-algebras of stable rank one and projective Hilbert modules Cuntz semigroups of C*-algebras of stable rank one and projective Hilbert modules

2010-01-26

arxiv.org/abs/1001.4558v3

Mathematics

Operator Algebras

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Scientific paper

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is compactly contained in $p$ to those in $q.$ It is also shown that every Hilbert module is projective in the category whose morphisms are bounded module maps with adjoints. A discussion of projective Hilbert modules (whose morphisms are bounded module maps) is also given.

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