Product integrals and inverses in normed rings
J.C. Helton · Pacific Journal of Mathematics · 1974
This paper concerns product integrals of functions with values in a normed complete ring.The inverses of elements obtained as such integrals are investigated.In particular, the conditions under which UΓP(1 + G)]" 1 exists are shown to be S y \G 2 \ = 0. Since the existence X of LPΓPU+G)]" 1 is connected with the existence of the product integrals Jp(l+G) and JK1 -G), the study of the inverse leads to a study of the conditions under which these integrals exist when x Yl v (l -f-G) is known to exist.Commutative and noncommutative rings are considered.