Given an operator ideal , we say that a Banach space X has the approximation property with respect to if T belongs to for every Banach space Y and every T ∈ (Y,X), being the topology of uniform convergence on compact sets. We present several characterizations of this type of approximation property. It is shown that some of the existing approximation properties in the literature may be included in this setting.
This note contains an approximation theorem that implies that every compact subset of is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.
Inspired by Pełczyński's decomposition method in Banach spaces, we introduce the notion of Schroeder-Bernstein quadruples for Banach spaces. Then we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.
We study the Orlicz type spaces Hω, defined as a generalization of the Hardy spaces Hp for p ≤ 1. We obtain an atomic decomposition of Hω, which is used to provide another proof of the known fact that BMO(ρ) is the dual space of Hω (see S. Janson, 1980, [J]).
This paper presents an elementary proof and a generalization of a theorem due to Abramovich and Lipecki, concerning the nonexistence of closed linear sublattices of finite codimension in nonatomic locally solid linear lattices with the Lebesgue property.
The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2),⎧ Δu + uq = 0, in Ω⎨⎩ u = μ, on ∂Ωwhere 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted Marcinkiewicz spaces.