Chapter 18 – Renormings of Banach Spaces

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