Abstract: 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.
Publication Year: 2010
Publication Date: 2010-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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