Vol. 48, No. 2, 1973

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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