On Amenability-Like Properties of a Class of Matrix Algebras. (6th April 2022)

• Record Type: Journal Article
• Authors: Rostami, M.; Shariati, S. F.; Sahami, A.
• Other Names: Rafeiro Humberto Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-04-06
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/3194715
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : In this study, we show that a matrix algebra ℒ ℳ I p A is a dual Banach algebra, where A is a dual Banach algebra and 1 ≤ p ≤ 2 . We show that ℒ ℳ I p ℂ is Connes amenable if and only if I is finite, for every nonempty set I . Additionally, we prove that ℒ ℳ I p 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 U p I p A ∗ ∗ is approximately biflat if and only if A ∗ ∗ is approximately biflat and I is a singleton.