THE SPACE L_q OF DOUBLE SEQUENCES

The spaces BS, BS(t), CS_p, CS_bp, CS_r and BV of double sequences have recently been studied by Altay and Ba¸sar [J. Math. Anal. Appl. 309(1)(2005), 70–90]. In this work, following Altay and Ba¸sar [1], we introduce the Banach space L_q of double sequences corresponding to the well-known space ℓ_q of single sequences and examine some properties of the space L_q. Furthermore, we determine the β(υ)-dual of the space and establish that the α- and γ-duals of the space L_q coincide with the β(υ)-dual; where 1 ≤ q < ∞ and υ 2 {p, bp, r}.