Abstract
In this section we point out some fundamental properties of linear operators in Banach spaces. The key assertions presented are the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Open Mapping Theorem, the Hahn-Banach Theorem, the Separation Theorem, the Eberlain-Smulyan Theorem and the Banach Theorem. We recall that the collection of all continuous linear operators from a normed linear space X into a normed linear space Y is denoted by \( \mathcal{L}\left( {X,{\mathbf{ }}Y} \right) \) , and \( \mathcal{L}\left( {X,{\mathbf{ }}Y} \right) \) is a normed linear space with the norm
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© 2007 Birkhäuser Verlag AG
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(2007). Properties of Linear and Nonlinear Operators. In: Methods of Nonlinear Analysis. Birkhäuser Advanced Texts / Basler Lehrbücher. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8147-9_2
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DOI: https://doi.org/10.1007/978-3-7643-8147-9_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8146-2
Online ISBN: 978-3-7643-8147-9
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