2020/04/22 by Elbour, Aziz
#46B07 (Primary) 46B42 #47B50 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2004.10691
In this paper, we investigate more about relationship between uaw -convergence (resp. un-convergence) and the weak convergence. More precisely, we characterize Banach lattices on which every weak null sequence is uaw-null. Also, we characterize order continuous Banach lattices under which every norm bounded un-null net (resp. sequence) is weakly null. As a consequence, we study relationship between sequentially uaw-compact operators and weakly compact operators. Also, it is proved that every continuous operator, from a Banach lattice E into a non-zero Banach space X, is unbounded continuous if and only if E′ is order continuous. Finally, we give a new characterization of b-weakly compact operators using the uaw-convergence sequences.