Basic Concepts of Functional Analysis

  • E. R. de Arantes e Oliveira
Part of the International Centre for Mechanical Sciences book series (CISM, volume 121)


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.


Hilbert Space Linear Space Orthogonal Projection Linear Subspace Normed Linear Space 
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Copyright information

© Springer-Verlag Wien 1975

Authors and Affiliations

  • E. R. de Arantes e Oliveira
    • 1
  1. 1.University of LisbonPortugal

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