Vector Valued Orlicz Sequence Space Generilazed with an Infinite Matrix and Some of its Specific Characteristics

The primary purpose of the present study is to present the vector valued sequence space F (A,Xk,M, p, s) and to study the closed subspace of it. Where, F is a normal sequence algebra with absolutely monotone norm ‖.‖F and having a Schauder base (ek) , where ek = (0, · · · , 0, 1, 0, · · · ) , with 1 in the k−th place; A is a nonnegative matrix; Xk is seminormed space over the complex field C with seminorm qk for each k ∈ N; M is an Orlicz function; p = (pk) be any sequence of strictly positive real numbers and s be any non-negative real number. We investigate important algebraic and topological characteristics of this space and also examine some inclusion relations on it. Our results are much more general than the corresponding results given by.