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Let be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If has the (iii)-property, then its completion is an order-complete locally solid lattice group. (2) If is order-complete and has the Fatou property, then the order intervals of are -complete. (3) If has the Fatou property, then is order-dense in and has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...
The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework...
We prove that every map T between two F*-spaces which preserves equality of distance and satisfies T(0) = 0 is linear.
We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g: X → ℝ, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral , considered as a function on the space of all T-invariant Borel probability measures μ, attains its maximum on a measure supported on a periodic orbit.
Several properties of the class of minimal Orlicz function spaces LF are described. In particular, an explicitly defined class of non-trivial minimal functions is shown, which provides concrete examples of Orlicz spaces without complemented copies of F-spaces.
In questa Nota viene stabilita una caratterizzazione generale della semicontinuità inferiore delle multifunzioni, a grafico convesso, definite in sottoinsieme non vuoto, aperto e convesso di uno spazio vettoriale topologico e a valori in uno spazio vettoriale topologico localmente convesso. Sono poste in luce, poi, varie conseguenze di tale caratterizzazione.
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