# Basic Concepts of Functional Analysis

Chapter

## Abstract

Let X and Y be arbitrary nonempty sets and suppose that some rule is given whereby to each element x ∈ X corresponds a uniquely determined element y ∈ Y which is called the image of x in Y. Consider the set F consisting of all ordered pairs (x,y) where x ∈ X and y is the corresponding element of Y. Such set of pairs is called a function or an operator on X into Y [21]. The set X is called the domain of the function and the set of the elements of Y corresponding to all the elements of X is called the range of the function.

## Keywords

Hilbert Space Linear Space Orthogonal Projection Linear Subspace Normed Linear Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Wien 1975