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- W1567142770 endingPage "835" @default.
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- W1567142770 abstract "This chapter discusses renorming a Banach space that consists of replacing the given norm that is usually provided by the very definition of the space, by another norm that may have better (or sometimes worse) properties of convexity or smoothness, or both. This operation is by nature geometric. The geometric intuition is frequently useful and a few pictures might help in understanding certain proofs. The analytical point of view is of course necessary and proofs usually rely on careful computations. Computing in Banach spaces is quite difficult, because certain spaces have no basis and, therefore, there is no hope to use co-ordinates in calculations. Most results in renorming theory rely on topological assumptions. Norms that enjoy good properties of convexity and/or smoothness can be computed under natural (and optimal) topological assumptions. These norms are frequently obtained by duality arguments and they are tightly connected with the linear structure." @default.
- W1567142770 created "2016-06-24" @default.
- W1567142770 creator A5074278380 @default.
- W1567142770 date "2001-01-01" @default.
- W1567142770 modified "2023-10-01" @default.
- W1567142770 title "Renormings of Banach Spaces" @default.
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