NORMED LINEAR SPACES

The concepts elaborated in the form of definitions, examples and properties
of a normed space and the functions defined on such spaces are discussed in
this chapter. The notion of the norm of a vector is a generalization of the
notion of length and it obeys some simple and natural geometric principles.
A vector space together with the norm defined for its elements is called a
nOr/ned space. Mappings defined on a ormed space into another normed
space are called operators or transformations. The concepts elaborated in the form of definitions, examples and properties
of a normed space and the functions defined on such spaces are discussed in
this chapter. The notion of the norm of a vector is a generalization of the
notion of length and it obeys some simple and natural geometric principles.
A vector space together with the norm defined for its elements is called a
nOr/ned space. Mappings defined on a ormed space into another normed
space are called operators or transformations.