A note on idempotents in finite AW*-factors (Q2781253)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A note on idempotents in finite AW*-factors |
scientific article; zbMATH DE number 1721000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on idempotents in finite AW*-factors |
scientific article; zbMATH DE number 1721000 |
Statements
A note on idempotents in finite AW*-factors (English)
0 references
19 March 2002
0 references
AW*-algebra
0 references
quasi-trace
0 references
idempotent
0 references
projection
0 references
dimension function
0 references
Let \(A\) be an AW\(^*\)-factor of type \(\text{II}_1\) let \(D\) be the dimension function on the set \({\mathcal P}(A)\) of projections on \(A\), and let \(Q\) be its extension to the quasi-trace on \(A\). The author uses a clever argument based upon the \(2\times 2\) matrix algebra \(M_2(A)\) over \(A\) to show that, for each idempotent \(a\) in \(A\) and all elements \(\lambda\) in \(\mathbb{C}\), \(Q(\lambda a)= \lambda D(e(a))\) where \(e(a)\) is the left support of \(a\).
0 references
