Description of orthogonal vector fields over W*-algebra of type I 2

Abstract

© 2015, Allerton Press, Inc. In the paper we give a characterization of a w*-continuous orthogonal vector field F over a W*-algebra of type I2 in terms of reductions of F on the center of the algebra. As an application we obtain a new proof of the assertion that an arbitrary w*-continuous orthogonal vector field over a W*-algebra of type I2 is stationary.