Inversion in a class of lattice-ordered algebras
Korovkinhüllen in Funktionenräumen.
La méthode d'interpolation complexe : applications aux treillis de Banach
Lattices with real numbers as additive operators [Book]
Les topologies sygma-Lebesgue sur C(X).
We prove that if X is a compact topological space which contains a nontrivial metrizable connected closed subset, then the vector lattice C(X) does not carry any sygma-Lebesgue topology.
Lions-Peetre reiteration formulas for triples and their applications
We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted -spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability...
Local/global uniform approximation of real-valued continuous functions
For a Tychonoff space , is the lattice-ordered group (-group) of real-valued continuous functions on , and is the sub--group of bounded functions. A property that might have is (AP) whenever is a divisible sub--group of , containing the constant function 1, and separating points from closed sets in , then any function in can be approximated uniformly over by functions which are locally in . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...
Minimal Reflexive Banach Lattices.
Nonatomic Lipschitz spaces
We abstractly characterize Lipschitz spaces in terms of having a lattice-complete unit ball and a separating family of pure normal states. We then formulate a notion of "measurable metric space" and characterize the corresponding Lipschitz spaces in terms of having a lattice complete unit ball and a separating family of normal states.
-абсолют и интегрируемые по Риману функции.
On completely monotone functions on C+(X).
On Co-Semigroups of Lattice Homomorphisms on a Banach Lattice.
On Measures Integrating All Functions of a Given Vector Lattice.
On some density theorems in regular vector lattices of continuous functions.
In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions de ned on a locally compact Hausdorff space, which we introduced and studied in [3,4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the so-called generalized af ne functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by...
On some ergodic properties for continuous and affine functions
Two problems posed by Choquet and Foias are solved:(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such thatfor each in , but does not converge to 0.
On the lattice boundary of Markov operators
On the lattice properties of invariant functions for Markov operators on C(X)
On the lattice structure of invariant functions for Markov operators on
On the Representation of Banach Lattices by Continuous Numerical Functions.
On the sequential order continuity of the -space.