Karakaya, Vatan; Altun, Fatma

We introduce a new sequence space which is defined by the operator W=(wnk) 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.