On Amenability-Like Properties of a Class of Matrix Algebras

M. Rostami, S. F. Shariati, A. Sahami and Humberto Rafeiro

Journal of Mathematics, 2022, vol. 2022, 1-7

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

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3194715

DOI: 10.1155/2022/3194715

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