arXiv subjects

A. N. Sherstnev

Publications and source records attributed to A. N. Sherstnev.

2 recordsLinked to original sources

arXiv2013

A characterization of orthogonal vector fields over ${\bf W^*}$-algebras of type ${\bf I_2}$

In the paper we give a characterization of a $w^*$-continuous orthogonal vector field $F$ over an $W^*$-algebra $\mathcal{N}$ of type $I_2$ in terms of reductions $F$ on the center of $\mathcal{N}$. As an application it is obtained a proof of the assertion that an arbitrary $w^*$-continuous orthogonal vector field over a $W^*$-algebra of type $I_2$ is stationary.

math.OA↗

arXiv2011

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

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 $μ$ such that $\|μ(p)\|^2= m(p)$ 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.

math.OA↗