Theorems of the Stone-Weierstrass type for lattices of uniformly continuous functions.
Topological properties and matrix transformations of certain ordered generalized sequence spaces.
Torsion classes and subdirect products of Carathéodory vector lattices
Trace inequalities for spaces in spectral duality
Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained.
Two theorems of functional analysis effectively equivalent to choice axioms
Type et cotype dans les espaces munis de structures locales inconditionnelles