@article {Zeltser:2001:0133-3852:223, author = "Zeltser M.", title = "Weak Sequential Completeness of beta-duals of Double Sequence Spaces", journal = "Analysis Mathematica", volume = "27", year = "2001", abstract = "

We consider dual pairs langE,E^β(ν)rang of double sequence spaces E and E^β(ν), where E^β(ν) is the beta-dual space of E with respect to the nu-convergence of double sequences for nu = p (Pringsheim convergence), bp (bounded p-convergence) and r (regular convergence). Motivated by Boos, Fleming and Leiger [3], we introduce two oscillating properties (signed P_OSCP(k), k isin {1,2}) for a double sequence space E such that the signed P_OSCP(1) guarantees the sigma(E^β(p), E)-sequential completeness of E^β(p), whereas the signed P_OSCP(2) implies the equalities E^β(r) = E^β(bp) = E^β(p) and the sigma(E^β(ν), E)-sequentialcompleteness of E^β(ν) for nu = bp and r.

", pages = "223-238(16)", url = "http://www.ingentaconnect.com/content/klu/anam/2001/00000027/00000003/00393311" }