Banach Spaces

  • Ole ChristensenEmail author
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Banach spaces form a special class of normed vector spaces. Compared with other normed spaces, Banach spaces have the advantage that it is easier to check that a sequence of vectors in the space is convergent. We give the formal definition of a Banach space in Section 3.1. As example of a Banach space we consider the set of continuous functions on a closed and bounded interval. Other important Banach spaces, the sequence spaces \(\ell^p(\mathbb{N})\), are introduced in Section 3.2. In Section 3.3 we continue the analysis of bounded linear operators initiated in Section 2.4.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

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