Sequentially compact sets in a class of generalized Orlicz spaces
In this paper, we will characterize sequentially compact sets in a class of generalized Orlicz spaces.
Sequentially Right Banach spaces of order
We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order , and those defined by the dual property, the sequentially Right Banach spaces of order for . These classes of Banach spaces are characterized by the notions of -limited sets in the corresponding dual space and subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space and a reflexive Banach space...
Sets of minimal points in L...(...0,1..., dt).
Sharp uniform convexity and smoothness inequalities for trace norms.
Simplexe mit streng monotoner Entropiezahlenfolge
Singlevaluedness of monotone operators on subspaces of GSG spaces
We extend Zajíček’s theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a -cone supported set.
Smith's counterexample about uniform rotundity in every direction.
It is an open question when the direct sum of normed spaces inherits uniform rotundity in every direction from the factor spaces. M. Smith [4] showed that, in general, the answer is negative. The purpose of this paper is to carry out a complete study of Smith's counterexample.
Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces
Smooth approximations without critical points
In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set...
Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm
Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm
There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.
Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)
We show that, if μ is a probability measure and X is a Banach space, then the space L¹(μ,X) of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that X has such a norm, and that if X admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then L¹(μ,X) has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.
Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm
First, we extend the criteria for smooth points of from [22] to the whole class of Musielak-Orlicz spaces. Next, we present criteria for very smooth and strongly smooth points of .
Smoothness in
Snarked sums of Banach spaces.
Sobczyk's theorems from A to B.
Sobczyk's theorem is usually stated as: every copy of c0 inside a separable Banach space is complemented by a projection with norm at most 2. Nevertheless, our understanding is not complete until we also recall: and c0 is not complemented in l∞. Now the limits of the phenomenon are set: although c0 is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l∞.
Sobre espacios de Banach localmente uniformemente rotundos.
Sobre los espacios de Banach que contienen a l1 como complementado.
Solution to a problem of S. Rolewicz
Some applications of geometry of Banach spaces to harmonic analysis