Deformations of infinite projections

Details Deformations of infinite projections Deformations of infinite projections

2006-05-18

arxiv.org/abs/math/0605515v3

Mathematics

Operator Algebras

Scientific paper

Let $A=(A_x)$ be a (semi-)continuous field of $C^*$-algebras over a compact
Hausdorff space $X$ and let $p=(p_x)$ be a projection in $A$ such that each
$p_x\in A_x$ is properly infinite ($x\in X$). Then $p$ is properly infinite if
the field $A$ is upper semi-continuous. However, $p$ can be finite if the field
is lower semi-continuous.

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