Space Of Affine Functions Research Articles

Weak* fixed point property and the space of affine functions

First we prove that if a separable Banach space X X contains an isometric copy of an infinite-dimensional space A ( S ) A(S) of affine continuous functions on a Choquet simplex S S , then its dual X ∗ X^* lacks the weak ∗ ^* fixed point property for nonexpansive mappings. Then, we show that the dual of a separable L 1 L_1 -predual X X fails the weak ∗ ^* fixed point property for nonexpansive mappings if and only if X X has a quotient isometric to some infinite-dimensional space A ( S ) A(S) . Moreover, we provide an example showing that “quotient” cannot be replaced by “subspace”. Finally, it is worth mentioning that in our characterization the space A ( S ) A(S) cannot be substituted by any space C ( K ) \mathcal {C}(K) of continuous functions on a compact Hausdorff K K .

Weakly analytic sets for function spaces

We define and study weakly analytic sets for function spaces. This concept generalizes the concept of weak analyticity for function algebras. We also define weak analyticity for the space of affine functions using the ideas of convexity. We show that it coincides with the same concept regarding it as a function space. We give several examples to illustrate the concepts.

A Negative Result on Multivariate Convex Approximation by Positive Linear Operators

We consider the problem of multivariate convex approximation by positive linear operators. LetEbe ak-dimensional compact convex set inRkwithk⩾2,Ω⊂Rkan open set containingE, and letL:C(E)→C1(Ω) be a positive linear operator. Our main result of this paper shows that ifLpreserves convexity and satisfiesLl=lonEfor alll∈P1(the space of affine functions), thenLis trivial (i.e.,Lf∈P1onEfor allf∈C(E)) andEis a simplex.

Weakly prime sets for function spaces

We define and study weakly prime sets for a function space and show that it coincides with the known concept of weakly prime sets for function algebras and spaces of affine functions.

Korovkin-type theorems for positive functionals in spaces of continuous affine functions

Si stabiliscono dei risultati concernenti la convergenza di reti di forme lineari positive verso una prefissata forma lineare positiva nel contesto di spazi di funzioni continue ed affini definite su un insieme convesso compatto. Si presentano degli esempi e delle applicazioni in spazi di funzioni continue, inC*-algebre di operatori su spazi di Hilbert e in spazi di Banach reticolati.

The Sequential Stability Index and Certain Spaces of Affine Functions

The Sequential Stability Index and Certain Spaces of Affine Functions

The sequential stability index and certain spaces of affine functions

A theorem of J. M. Anderson and J. E. Jayne on the existence of uniformly closed linear subspaces of the space C 1 ( X ) {C^1}(X) of bounded Baire- 1 1 functions on the compact Hausdorff space X X having specified sequential stability index α > Ω \alpha > \Omega is here adapted and extended to yield similar theorems for certain spaces of Baire-affine functions defined on a compact Choquet simplex.

Properties of subspaces of the space of affine functions

Conditions are presented for weak (strong) convergence, in the entire space A(x), of a sequence of positive operators to a fixed operator S on the basis of its weak (strong) convergence to S in a subspace. The criterion of Bauer's simplex is presented.