On Some Geometric Properties of a New Paranormed Sequence Space

Abstract

We introduce a new sequence space which is defined by the operator W = (w(nk)) on the sequence space l(p). We define a modular functional on this space and investigate structure of this space equipped with Luxemburg norm. Also we study some geometric properties which are called Kadec-Klee, k-NUC, and uniform Opial properties and prove that this new space possesses these properties.