Abstract
The purpose of this paper is to discover and examine a four-dimensional Pascal matrix domain on Pascal sequence spaces. We show that they are spaces and also establish their Schauder basis, topological properties, isomorphism and some inclusions.
Highlights
It is well known that A = is a triangular matrix if amnjk = 0 for j > m, k > m or both, and amnjk ≠ 0 for all m, n ∈ N
2002) where the authors declared that there was no reason, whatsoever, to stop at a finite matrix of this type for, one can extend the Pascal matrix of finite order to an infinite lower triangular matrix
We introduce the extensions of the spaces p∞, pc, and p0 denoted by p∞2, pc[2], pb2c and p02 as the collections of all double sequences such that each P −transform of them are in the spaces l∞2, c2, cb[2] and c02 respectively; as follows: m,n p2 = {x = (x ) ∈ ω2: sup | ∑ ( m ) ( n ) x |
Summary
Let X and Y be two double sequence spaces and A = This paper will wish to introduce Pascal double sequence spaces, p∞2 , pc[2], pb2c and p02 as matrix domains of four-dimensional Pascal matrix, but, first we define the fourdimensional Pascal matrix P = (pmjkn) as follows: m n pjk = {(m − j) (n − k) , 0 ≤ j ≤ m, 0 ≤ k ≤ n (2)
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