Feynman's operational calculus for families of noncommuting operators: tensor products, ordered supports, and the disentangling of an exponential factor (Q1810011)

In the early 1950s, R. Feynman proposed operational calculus as a kind of generalized path integral. Feynman was especially concerned with exponentiating sums of noncommuting operators. The main result of the paper under review is a mathematically rigorous formulation and proof of Feyman's formula and some related formulas for systems of not necessarily commuting bounded linear operators acting on a Banach space. This paper is closely related to the recent paper by the same authors [Russ. J. Math. Phys. 8, 153-171 (2001; Zbl 1027.46002)] and the monograph ``The Feynman integral and Fenman's operational calculus'' by \textit{G. W. Johnson} and \textit{M. Lapidus} [Oxford Mathematical Monographs, Clarendon Press, Oxford (2000; Zbl 0952.46044)].