A Class of Reflexive Symmetric Bk-Spaces

Abstract

We denote by ω the linear space of all sequences of real or complex numbers. A linear subspace of ω is called a sequence space . A sequence space E is a BK-space ( 9 ) if it is equipped with a norm under which: first, E is a Banach space and second, each of the coordinate maps x → x i is continuous. Let ∑ be the group of all permutations of Z + = {1, 2, 3, …}. If x ∈ ω and σ ∈ ∑ , the sequence x σ is defined by ( x σ ) i = x σ( i ) ). A sequence space E is symmetric if x σ ∈ E whenever x ∈ E and σ ∈ ∑ . Accounts of symmetric sequence spaces occur in ( 3; 7; 8 ).