Vol. 30, No. 2, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Homomorphisms of annihilator Banach algebras. II

Gregory Frank Bachelis

Vol. 30 (1969), No. 2, 283–291
Abstract

Let A be a semi-simple annihilator Banach algebra, and let ν be a homomorphism of A into a Banach algebra. In this paper it is shown that there exists a constant K and dense two-sided ideals containing the socle, IL and IR, such that ν(xy)Kx∥⋅∥ywhenever x IL or y IR. If A has a bounded left or right approximate identity, then ν is continuous on the socle. Thus if A = L1(G), where G is a compact topological group, then any homomorphism of A into a Banach algebra is continuous on the trigonometric polynomials.

Mathematical Subject Classification
Primary: 46.50
Milestones
Received: 17 January 1969
Published: 1 August 1969
Authors
Gregory Frank Bachelis