ON THE TAYLOR SEQUENCE SPACES OF NONABSOLUTE TYPE WHICH INCLUDE THE SPACES c(0) AND c

Abstract

Let T(r) denotes the Taylor method of order r such that r is an element of C/{0}. In this paper, we introduce Taylor sequence spaces t(0)(r) and t(c)(r) consisting of all sequences whose T(r)-transforms are in the spaces c(0) and c. We investigate some properties and compute alpha-, beta- and gamma-duals of these spaces. Afterwards, we characterize of some matrix classes of Taylor sequence spaces t(0)(r) and t(c)(r) and give Steinhaus type theorems.