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Orlicz sequence spaces of four dimensional regular matrix and their closed ideal. (English) Zbl 1465.46007

Summary: In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrix \(A = (a_{rtkl})\). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space \(l^2_\infty\).

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
40F05 Absolute and strong summability
40B05 Multiple sequences and series
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