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Two problems posed by Choquet and Foias are solved:(i) Let $T$ be a positive linear operator on the space $C (X)$ of continuous real-valued functions on a compact Hausdorff space $X$ . It is shown that if $n^{- 1} \sum_{r = 0}^{n - 1} T^{r} 1$ converges pointwise to a continuous limit, then the convergence is uniform on $X$ .(ii) An example is given of a Choquet simplex $K$ and a positive linear operator $T$ on the space $A (K)$ of continuous affine real-valued functions on $K$ , such that $\inf {(T^{n} 1) (x) : n \geq} < 1$ for each $x$ in $\partial_{ℓ} K$ , but $∥ T^{n} 1 ∥$ does not converge to 0.

Displaying 1 – 13 of 13

On 2-strong homomorphisms and 2-normed hypersets in hypervector spaces.

On a class of convex sets

On best simultaneous approximation.

On Certain Topologies on a Vector Space.

On Farkas-type theorems

On measures of noncompactness in general topological vector spaces

On norms and subsets of linear spaces

On Schwartz Spaces and Mackey Convergence

On semi-inner product spaces, II

On some ergodic properties for continuous and affine functions

On some properties of hyperconvex spaces.

On subdifferential calculus and duality in non-convex optimization

On the Permanence of the Hahn-Banach Property in Bornology

Currently displaying 1 – 13 of 13