On the extension of positive operators
We prove that every locally quasi-convex Schwartz group satisfies the Glicksberg theorem for weakly compact sets.
In this note we obtainsome strong barrelledness properties concerning the simple function space generated by the hereditary ring Z of a11 subsets of density zero of N.
We introduce the notions of pointwise modulus of squareness and local modulus of squareness of a normed space X. This answers a question of C. Benítez, K. Przesławski and D. Yost about the definition of a sensible localization of the modulus of squareness. Geometrical properties of the norm of X (Fréchet smoothness, Gâteaux smoothness, local uniform convexity or strict convexity) are characterized in terms of the behaviour of these moduli.
Necessary and sufficient conditions for URWC points and LURWC property are given in Orlicz sequence space lM.