Titlebook: Renormings in Banach Spaces; A Toolbox Antonio José Guirao,Vicente Montesinos,Václav Zizl Book 2022 The Editor(s) (if applicable) and The A

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Renormings in Banach Spaces978-3-031-08655-7Series ISSN 0077-0507 Series E-ISSN 2297-0274

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Norms, normed spaces, Banach spacesIn this chapter we will set the basic definitions —and some results, with their references— that will be used along the text. We include them here in order to avoid repetitions later on. For further information, the reader may access any of the texts mentioned in the references.

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Some structural properties of Banach SpacesIn this chapter we shall introduce, for later references, some structures in a Banach space that allow for vector representation and computations —a coordinate system—, and consequent classification of spaces in such terms. They will also allow for renormings of the Banach space or its dual.

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