International Journal of Nonlinear Analysis and Applications

On left ϕ-Connes biprojectivity of dual Banach algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran

2 Department of Mathematics, University of Kurdistan, Pasdaran Boulevard, Sanandaj 66177--15175, P. O. Box 416, Iran

3 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

4 Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, P.O.Box 94531, Iran

Abstract

We introduce the notion of left (right) ϕ-Connes biprojective for a dual Banach algebra A, where ϕ is a non-zero wk∗-continuous multiplicative linear functional on A. We discuss the relationship of left ϕ-Connes biprojectivity with ϕ-Connes amenability and Connes biprojectivity. For a unital weakly cancellative semigroup S, we show that ℓ1(S) is left ϕS-Connes biprojective if and only if S is a finite group, where  ϕS∈Δw∗(ℓ1(S)). We prove that for a non-empty totally ordered set I with the smallest element, the upper triangular I×I-matrix algebra UP(I,A) is right ψϕ-Connes biprojective if and only if A is right ϕ-Connes biprojective and I is a singleton, provided that A has a right identity and ϕ∈Δw∗(A). Also for a finite set I,  if Z(A)∩(A−ker⁡ϕ)≠∅, then the dual Banach algebra UP(I,A) under this new notion forced to have a singleton index

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 257-264
  • Receive Date: 04 June 2021
  • Revise Date: 05 September 2021
  • Accept Date: 08 October 2021