On spaces derivable from a solid sequence space and a non-negative lower triangular matrix

İngilizce (OpenAlex)

The scalar field will be either the real or complex numbers. Suppose that is a solid sequence space over the scalar field and A is an infinite lower triangular matrix with non-negative entries and positive entries on the main diagonal such that each of its columns is in . For each positive integer k , the k th predecessor of with respect to A is the solid vector space of scalar sequences x such that A k |x| is an element of . We denote this space by k and itself will be denoted by 0 . Under reasonable assumptions, these spaces inherit some topological properties from . We are interested in a projective limit of the infinite product of the k consisting of sequences of sequences (x (k) ) satisfying Ax (k) = x (k-1) for each k > 0 . We show that for interesting classes of situations including the cases when = l p for some p > 1 and A is the Cesro matrix, the space of our interest can be non-trivial.