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Banach Spaces

  • Carlos S. Kubrusly
Chapter

Abstract

Our purpose now is to put algebra and topology to work together. For instance, from algebra we get the notion of finite sums (either ordinary or direct sums of vectors, linear manifolds, or linear transformations), and from topology the notion of convergent sequences. If algebraic and topological structures are suitably laid on the same underlying set, then we may consider the concept of infinite sums and convergent series. More importantly, as continuity plays a central role in the theory of topological spaces, and linear transformation plays a central role in the theory of linear spaces, when algebra and topology are properly combined they yield the concept of continuous linear transformation; the very central theme of this book.

Keywords

Banach Space Linear Space Normed Space Topological Vector Space Linear Manifold 
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 Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentCatholic University of Rio de JaneiroRio de JaneiroBrazil

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