Snarked sums of Banach spaces.
Sobczyk's theorem and the Bounded Approximation Property
Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.
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∞.
Sobolev Type Embeddings in the Limiting Case.
Sobre espacios de Banach localmente uniformemente rotundos.
Sobre L-órdenes entre t-normas estrictas.
Several order relations in the set of strict t-norms are investigated.
Sobre los espacios de Banach que contienen a l1 como complementado.
Sobre los espacios de Orlicz de funciones vectoriales.
Sobre los teoremas de Lyapunov y de Radon-Nikodym.
Sobre sumabilidad Cesáro en el espacio CS (I).
Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces.
Solution to a problem of S. Rolewicz
Solutions of .
Solvability of a recursive functional equation in the sequence Banach space.
Solvability of an Infinite System of Singular Integral Equations
2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
Some applications of geometry of Banach spaces to harmonic analysis
Some applications of martingales in Banach spaces
Some applications of p-summing operators to Banach space theory
Some Applications of Simons’ Inequality
We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.
Some approximation results in Musielak-Orlicz spaces
We prove the continuity in norm of the translation operator in the Musielak-Orlicz spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in , in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.