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.
