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.


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