Some Topological and Geometrical Properties of New Banach Sequence Spaces

Abstract

In the present paper, we introduce a new band matrix (F) over cap and define the sequence space

l(p)((F) over cap) = {x = (x(k)) is an element of omega : Sigma(k) vertical bar f(k)/f(k+1) x(k) - f(k+1/)f(k) x(k-1)vertical bar(p) < infinity; 1 <= p <= infinity},

where f(k) is the kth Fibonacci number for every k is an element of N. We also establish some inclusion relations concerning this space and determine its alpha-, beta-, gamma-duals. Further, we characterize some matrix classes on the space l(p)(<(F)over cap>) and examine some geometric properties of this space.