whenever a belongs to the closed convex hull of the set of weak limit points of {an}∞n=1. In case X has the Banach-Saks property and {an}∞n=1 is bounded the converse assertion holds too. A characterization of reflexive spaces in terms of limit points and cores of bounded sequences is also given. The motivation for the problems investigated goes back to Lévy laplacian from potential theory in Hi...

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms weakly null nets, we introduce unbounded operators replacing weak convergence with absolutely (uaw-convergence) lattices. We characterize order lattices and reflexive these operators. Moreover, motivated characterizing lattice Cauchy sequences, consider pre-unbounded which maps uaw-Cauchy sequences to...