Subseries convergence and localization properties in sequence spaces supported by ideals in

We investigate various Localization Properties of ideals in relative to sequence spaces supported by them, particularly the Localization Property for Series . The results obtained enable us to prove the existence of a class of sequence spaces X in which every zero-density convergent series is subseries convergent (i.e., X has the Zero Density Convergence Property ), but some lacunary convergent series are not (i.e., X fails the Lacunary Convergence Property ).