The second dual spaces of the sets of Λ-strongly convergent and bounded sequences

Abstract

We give the second β-, γ-, and f-duals of the sets w0p(Λ), w∞p(Λ)(0<p<∞), c0p(Λ), cp(Λ), and c∞p(Λ)(0<p≤1) and the second continuous dual spaces of w0p(Λ), c0p(Λ), and cp(Λ) for 0<p≤1. Furthermore, we determine the α-duals of c0p(Λ), cp(Λ), and c∞p(Λ) for 1<p<∞.

Keywords

• BK spaces
• AK spaces
• AD spaces
• dual spaces.