[EN] It is a classical fact, due to Day, that every separable Banach space admits an equivalent Gateaux smooth renorming. In fact, it admits an equivalent uniformly Gateaux smooth norm, as was shown later by Day, James, ...
Guirao Sánchez, Antonio José; Hajek, P.(American Mathematical Society, 2007-06-22)
[EN] It is known that, given a Banach space (X, parallel to center dot parallel to), the modulus of convexity associated to this space delta X is a non-negative function, nondecreasing, bounded above by the modulus of ...
Guirao Sánchez, Antonio José; Hajek, P.(Springer-Verlag, 2007-11)
[EN] Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone.
[EN] Given a Banach space (X,k · k), we study the connection between uniformly
convex functions f : X ¿ R bounded above by k · kp
, and the existence of norms on
X with moduli of convexity of power type. In particular, we ...