Weak Sequential Completeness of -duals of Double Sequence Spaces

Abstract:

We consider dual pairs E,E^β(ν) of double sequence spaces E and E^β(ν), where E^β(ν) is the -dual space of E with respect to the -convergence of double sequences for = 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 {1,2}) for a double sequence space E such that the signed P_OSCP(1) guarantees the (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 (E^β(ν), E)-sequentialcompleteness of E^β(ν) for = bp and r.

Language: English

Document Type: Regular paper

Affiliations: 1: University of Tartu Vanemuise 46, R.250 Tartu, 51 014 Estonia