On some geometric properties of a new paranormed sequence space (Q2249984)

Summary: We introduce a new sequence space which is defined by the operator \(W=(w_{nk})\) on the sequence space \(\ell(p)\). We define a modular functional on this space and investigate the structure of this space equipped with the 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.