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Choice principles in Węglorz’ models

N. Brunner, Paul Howard, Jean Rubin (1997)

Fundamenta Mathematicae

Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.

Choquet simplexes whose set of extreme points is K -analytic

Michel Talagrand (1985)

Annales de l'institut Fourier

We construct a Choquet simplex K whose set of extreme points T is 𝒦 -analytic, but is not a 𝒦 -Borel set. The set T has the surprising property of being a K σ δ set in its Stone-Cech compactification. It is hence an example of a K σ δ set that is not absolute.

Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives

Paweł Domański (2004)

Banach Center Publications

This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...

Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations

Michel Talagrand (1982)

Annales de l'institut Fourier

Let G be a locally compact group. Let L t be the left translation in L ∞ ( G ) , given by L t f ( x ) = f ( t x ) . We characterize (undre a mild set-theoretical hypothesis) the functions f ∈ L ∞ ( G ) such that the map t → L t f from G into L ∞ ( G ) is scalarly measurable (i.e. for φ ∈ L ∞ ( G ) * , t → φ ( L t f ) is measurable). We show that it is the case when t → θ ( L f t ) is measurable for each character θ , and if G is compact, if and only if f is Riemann-measurable. We show that t → L t f is Borel measurable if and only if f is left uniformly continuous.Some of the measure-theoretic tools used there...

Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet, A. Defant, A. Peris, M. Ramanujan (1994)

Studia Mathematica

We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from l p to l q . Several sharp forms of this result are also included.

Common extensions for linear operators

Rodica-Mihaela Dăneţ (2011)

Banach Center Publications

The main meaning of the common extension for two linear operators is the following: given two vector subspaces G₁ and G₂ in a vector space (respectively an ordered vector space) E, a Dedekind complete ordered vector space F and two (positive) linear operators T₁: G₁ → F, T₂: G₂ → F, when does a (positive) linear common extension L of T₁, T₂ exist? First, L will be defined on span(G₁ ∪ G₂). In other results, formulated in the line of the Hahn-Banach extension theorem, the common...

Currently displaying 441 – 460 of 2679