Silov Boundaries of Spaces of Functions with Noncompact Domains.
Simplexe mit streng monotoner Entropiezahlenfolge
Simultaneous automorphisms on the space of analytic functions of several complex variables
Simultaneous resolutions of the identity operator in normed spaces.
We construct in this paper some simultaneous projective resolutions of the identity operator which we later use to obtain certain new results on quasi-complementation property and Markushevich bases.
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.
Slice-products in bivariate approximation
Smallest singular value of sparse random matrices
We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances of the entries....
Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces
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 partitions of unity in preduals of WCG spaces.
Smooth partitions of unity on some non-separable Banach spaces
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 .
Smoothability versus dentability
Smoothness in Banach spaces. Selected problems.
This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and get a feeling about this area of Banach space theory. Many open problems of different level of difficulty are discussed. For the reader...
Smoothness in