Weak Sequential Completeness of -duals of Double Sequence Spaces

Author: Zeltser M.¹

Source: Analysis Mathematica, Volume 27, Number 3, 2001 , pp. 223-238(16)

Publisher: Springer

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Abstract:

We consider dual pairs lang E,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 -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 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 = bp and r.