Matrix Mappings on the Domains of Invertible Matrices

Abstract EN

We focus on sequence spaces which are matrix domains of Banach sequence spaces.

We show that the characterization of a random matrix operator T=(tnk)∈(EA,FB), where EA and FB are matrix domains with invertible matrices A and B, can be reduced to the characterization of the operator S=B∘T∘A−1∈(E,F).

As an application, the necessary and sufficient conditions for the matrix operators between invertible matrix domains of the classical sequence spaces and norms of these operators are given.