Algebras of operator sequences

Abstract

Now we change our topic and move from operator theory to numerical analysis. In this chapter, X is a Banach space (which will be separable and of infinite dimension in all actual settings that we consider), I is the identity operator on X, ${\mathcal{L}} (X)$ is the Banach algebra of all bounded linear operators on X, and ${\mathcal{K}}(X)$ is the ideal of the compact operators in ${\mathcal{L}}(X)$.