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

Dutta, H.

Vladikavkaz. Mat. Zh. 13, No. 2, 26-34 (2011).

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

Keywords:

difference sequence; 2-norm; Orlicz function; paranorm; completeness; solidity; symmetry; convergence freeness; monotone space