In this article, we show that a matrix algebra LMp I (A) is a dual Banach algebra, where A is a dual Banach algebra and 1 ≤ p ≤ 2. We show that LMp I (C) is Connes amenable if and only if I is finite, for every non-empty set I. Additionally, we prove that LMp I (C) is always pseudo-Connes amenable for 1 ≤ p ≤ 2. Also Connes amenability and approximate Connes biprojectivity are investigated for generalized upper triangular matrix algebras. Finally, we show that UPp I (A) ∗∗ is approximately biflat if and only if A ∗∗ is approximately biflat and I is a singleton.
