Operators in Finite-Dimensional Normed Spaces

Abstract

We consider an n-dimensional (with 0 < n < ∞ )linear space E (referred to as the ground or basic space) over the field ℝ or ℂ of real or, respectively, complex numbers. The notations E and n for the ground space and its dimensions will be kept fixed throughout the book. In studying questions that can be treated without making distinction between the real and complex case we shall denote the ground field by K. As a rule, the ele-ments of K (scalans) will be denoted by lowercase Greek letters, and the elements of the ground space E (vectons) by lowercase Roman letters. The maps E → K and E → E are called bunctionals on E and, respectively, openatons in E. Linean bunctionals and openatons are defined in the usual manner. The adjective “linear” is omitted whenever the linearity is plain from the context. From now on the standard language of linear algebra will be used without superfluous explanations.