Semidifferential calculus.
Semireflexive Spaces In Which The Theorem On The Derivative-Of-The-Inverse Fails For Frechet Derivatives.
Semivariation in -spaces
Suppose that and are Banach spaces and that the Banach space is their complete tensor product with respect to some tensor product topology . A uniformly bounded -valued function need not be integrable in with respect to a -valued measure, unless, say, and are Hilbert spaces and is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index and suppose that and are -spaces with the associated -tensor product...
Separability of analytic images of some Banach spaces
Separable quotients of Banach spaces.
In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.
Separating polynomials on Banach spaces.
In this paper we survey some recent results concerning separating polynomials on real Banach spaces. By this we mean a polynomial which separates the origin from the unit sphere of the space, thus providing an analog of the separating quadratic form on Hilbert space.
Sequential compactness for the weak topology of vector measures in certain nuclear spaces.
Sequential convergences and Dunford-Pettis properties.
Set valued measures and integral representation
The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.
Sets with the Radon-Nikodým property in conjugate Banach space
Shilov boundary for holomorphic functions on some classical Banach spaces
Let be the Banach space of all bounded and continuous functions on the closed unit ball of a complex Banach space X and holomorphic on the open unit ball, with sup norm, and let be the subspace of of those functions which are uniformly continuous on . A subset is a boundary for if for every . We prove that for X = d(w,1) (the Lorentz sequence space) and X = C₁(H), the trace class operators, there is a minimal closed boundary for . On the other hand, for X = , the Schreier space,...
Smallness of sets of nondifferentiability of convex functions in non-separable 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 measures, the Malliavin calculus and approximations in infinitedimensional spaces
Smooth partitions of unity in preduals of WCG spaces.
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 of a typical convex function
Sobolev type inequalities for p>0
Sobolev's and local derivatives
Sobre el teorema de Dieudonné-Cirothendieck.