THE SPACE L q OF DOUBLE SEQUENCES

Abstract

The spaces BS, BS(t), CSp, CSbp, CSr and BV of double 
\nsequences have recently been studied by Altay and Başar [J. Math. Anal.
\nAppl. 309(1)(2005), 70–90]. In this work, following Altay and Başar [1],
\nwe introduce the Banach space Lq of double sequences corresponding to
\nthe well-known space ℓq of single sequences and examine some properties
\nof the space Lq. Furthermore, we determine the β(υ)-dual of the space
\nand establish that the α- and γ-duals of the space Lq coincide with the
\nβ(υ)-dual; where 1 ≤ q < ∞ and υ ∈ {p, bp, r}.