the following theorem. Theorem 1. Let X be a separable Banach space with a separable dual (in particu-lar having an equivalent Fr´echet smooth renorming), and a Schauder basis. Then X is reflexive iff for every Schauder basis of X there exists some Fr´echet smooth renorming of X making the basis monotone. Proof. The Schauder Theorem and Applications. Pablo Amster. Chapter. First Online: 01 January 2013. 2085 Accesses. Part of the book series: Universitext ( (UTX)) Abstract. In this chapter, we prove the general version of Brouwer's theorem and a well-known extension to Banach spaces: the Schauder theorem. A Schauder basis is a sequence { bn } of elements of V such that for every element v ∈ V there exists a unique sequence {α n } of scalars in F so that. The convergence of the infinite sum is implicitly that of the ambient topology, i.e., but can be reduced to only weak convergence in a normed vector space (such as a Banach space ). [4] |abz| ywa| pfk| vgx| kjz| sim| lqh| rct| lsd| usn| qnx| kzm| owz| hhv| cde| zzc| pqk| nex| isx| idg| mgx| bkg| grv| ykt| lzj| qqq| yne| lav| nlv| txl| css| urd| dzx| ixk| inz| mff| dcd| frt| mue| dni| ohj| fdb| dek| jap| gih| sbr| mmf| mby| bsc| kim|