Measures on projections in a $W^*$-algebra of type $I_2$

Details Measures on projections in a $W^*$-algebra of type $I_2$ Measures on projections in a $W^*$-algebra of type $I_2$

2011-12-23

arxiv.org/abs/1112.5569v1

Mathematics

Operator Algebras

8 pages

Scientific paper

It is shown that for every measure $m$ on projections in a $W^*$-algebra of
type $I_2$, there exists a Hilbert-valued orthogonal vector measure $\mu$ such
that $\|\mu(p)\|^2= m(p)$ for every projection $p$. With regard to J.
Hamhalter's result (Proc. Amer. Math. Soc., 110 (1990), 803-806) it means that
the assertion is valid for an arbitrary $W^*$-algebra.

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