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Some vector valued multiplier difference sequence spaces defined by a sequence of Orlicz functions. (English) Zbl 1242.46010

Summary: We introduce some new difference sequence spaces with a real 2-normed linear space as base space and which are defined using a sequence of Orlicz functions, a bounded sequence of positive real numbers and a sequence of non-zero reals as multiplier sequence. We show that these spaces are complete paranormed spaces when the base space is a 2-Banach space and investigate these spaces for solidity, symmetry, convergence freeness, monotonicity and sequence algebra. Further we obtain some relations between these spaces and prove some inclusion results.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
40A05 Convergence and divergence of series and sequences
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