Physikalische Mathematik

Histories Distorted by Partial Isometries

Abstract

Ilwoo Cho

In quantum dynamical systems, a history is defined by a pair (M,?), consisting of a type I factor M, acting on a Hilbert space H, and an E0-group ? = (?t)t?R, satisfying certain additional conditions. In this paper, we distort a given history (M,?), by a finite family G of partial isometries on H. In particular, such a distortion is dictated by the combinatorial relation on the family G. Two main purposes of this paper are (i) to show the existence of distortions on histories, and (ii) to consider how distortions work. We can understand Sections 3, 4 and 5 as the proof of the existence of distortions (i), and the properties of distortions (ii) are shown in Section 6. MSC 2010: 05C21, 05C25, 16T20, 22A22, 46N50, 47L15, 47L75, 47L90, 81Q12.