SOME NEW SEQUENCE SPACE SDEFINED BY A MODULUS FUNCTION AND AN INFINITE MATRIX IN A SEMINORMED SPACE

Let (c) over cap denotes the space of almost convergent sequences introduced by G. G. Lorentz [A contribution to the theory of divergent sequences, Acta Math. 8 0 ( 1948), 167{190]. The main purpose of the present paper is to introduce the sequence spaces w 0 ((A) over cap .p; f; q; s); w ((A) over cap ,p; f; q; s) and w(infinity) ((A) over cap ,p; f; q; s) defined by a modulus function f. Some topological properties of that spaces are examined. Also we exposed some inclusion relations among the variations of the space.