Vol. 51, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Product integrals and inverses in normed rings

Jon Craig Helton

Vol. 51 (1974), No. 1, 155–166
Abstract

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 [x y(1 + G)]1 exists are shown to be related to the requirement that xy|G2| = 0. Since the existence of [x y(1 + G)]1 is connected with the existence of the product integrals y x(1 + G) and x y(1 G), the study of the inverse leads to a study of the conditions under which these integrals exist when x y(1 + G) is known to exist. Commutative and noncommutative rings are considered.

Mathematical Subject Classification 2000
Primary: 46H99
Secondary: 46G99
Milestones
Received: 31 October 1972
Published: 1 March 1974
Authors
Jon Craig Helton