On some properties of Banach operators. II

Using the notion of a Banach operator, we have obtained a decompositional property of a Hilbert space, and the equality of two invertible bounded linear multiplicative operators on a normed algebra with identity. 1. Introduction. This paper is a continuation of our earlier work [7] on Banach operators. We recall that if X is a normed space and α : X → X is a mapping, then following [4], α is said to be a Banach operator if there exists a constant k such that 0 ≤ k < 1 and α 2 (x) − α(x) ≤ kα(x) − x for all x ∈ X. Banach operators are generalizations of