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\(I\)-convergent sequence spaces associated with multiplier sequences. (English) Zbl 1167.46005

Summary: We introduce the sequence spaces \(c^I(\Lambda)\), \(c^I_0(\Lambda)\), \(m^I(\Lambda)\) and \(m^I_0(\Lambda)\) associated with the multiplier sequence \(\Lambda = (\lambda k)\) of nonzero scalars. We study the different algebraic and topological properties of these sequence spaces like solidness, symmetricity, sequence algebra, convergence free, etc. Also, we characterize the multiplier problem and obtain some inclusion relation involving these sequence spaces.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
40A05 Convergence and divergence of series and sequences
40C05 Matrix methods for summability
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