Vol. 48, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Contractors, approximate identities and factorization in Banach algebras

Mieczyslaw Altman

Vol. 48 (1973), No. 2, 323–334
Abstract

The concept of a contractor has been introduced as a tool for solving equations in Banach spaces. In this way various existence theorems for solutions of equations have been obtained as well as convergence theorems for a broad class of iterative procedures. Moreover, the contractor method yields unified approach to a large variety of iterative processes different in nature. The contractor idea can also be exploited in Banach algebras.

A contractor is rather weaker than an approximate identity. Since every approximate identity is a contractor, the following seems to be a natural question: When is a contractor an approximate identity? The answer to this question is investigated in the present paper.

Mathematical Subject Classification 2000
Primary: 46H05
Milestones
Received: 1 March 1972
Published: 1 October 1973
Authors
Mieczyslaw Altman