Kadison Transitivity (Used in §6) - Imported Knowlpedia Content

A form of Kadison's theorem used in §6: if $\mathfrak A$ acts irreducibly on $\mathcal H$ and $x,y\in\mathcal H$ , then there exists $A\in\mathfrak A$ with $Ax=y$ .

Remarks

Key property (paper use):

Lets Shale characterize "relative normalizability" of states via $F(X)=E(A^*XA)$ .

Examples

In $B(\mathcal H)$ , take $A$ to be a rank-one operator sending $x$ to $y$ .