Positivity https://doi.org/10.1007/s11117-018-0620-3 Positivity On the difference spaces of almost convergent and strongly almost convergent double sequences Hüsamettin Çapan 1 · Feyzi Ba¸ sar 2,3 Received: 5 October 2017 / Accepted: 11 October 2018 © Springer Nature Switzerland AG 2018 Abstract In this paper, we study the difference spaces F (Δ), F 0 (Δ), [F ](Δ) and [F ] 0 (Δ) of double sequences obtained as the domain of four-dimensional backward difference matrix Δ in the spaces F , F 0 , [F ] and [F ] 0 of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We exam- ine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces. Keywords Double sequence · Almost convergence · Strongly almost convergence · Difference sequence space · Dual space Mathematics Subject Classification 46A45 · 40C05 1 Introduction and notations By Ω, we denote the set of all complex valued double sequences, i.e. Ω :=  x = (x kl ) : x kl ∈ C for all k , l ∈ N  The main results of this paper were presented at International Conference of Mathematical Sciences (ICMS 2018) to be held 31 July–06 August 2018 at Maltepe University, ˙ Istanbul, Turkey. B Feyzi Ba¸ sar feyzibasar@gmail.com Hüsamettin Çapan husamettincapan@gmail.com 1 ˙ Istanbul University, Beyazıt Campus, 34134 ˙ Istanbul, Turkey 2 ˙ Inönü University, 44280 Malatya, Turkey 3 Present Address: KısıklıMah. Alim Sok, Alim Apt. No: 7/6, 34692 Üsküdar, ˙ Istanbul, Turkey 123