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 → xi is continuous. Let ∑ be the group of all permutations of Z+ = {1, 2, 3, …}. If x ∈ ω and σ ∈ ∑, the sequence xσ is defined by (xσ)i = xσ(i)). A sequence space E is symmetric if xσ ∈ E whenever x ∈ E and σ ∈ ∑. Accounts of symmetric sequence spaces occur in (3; 7; 8).