|
چکیده
|
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 ` 1 (S) is left φS-Connes biprojective if and only if S is a finite group, where φS ∈ ∆w∗ (` 1 (S)). We prove that for a non-empty totally ordered set I with a 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 singleton, provided that A has a right identity and φ ∈ ∆w∗ (A). Also for a finite set I, if Z(A)∩(A −ker φ) 6= ∅, then the dual Banach algebra UP(I, A) under this new notion forced to have a singleton index.
|