φ-Splitting of Short Exact Sequences and φ-Connes Amenabilityof Some Banach Algebras

Let φ and ψ be w*-continuous homomorphisms from dualBanach algebras 𝐴 and 𝐵 to ℂ. In this paper, we presentsome characterizations of φ-Connes amenability and ψ-Connes amenability of dual Banach algebra A and Bwith preduals 𝐴∗ and 𝐵∗, respectively in terms of so-called φ-splitting and ψ-splitting of the short exactsequences. Also, we investigate the relation between φ-splitting of the certain short exact sequence and φ-σwcvirtual diagonal of a Banach algebra. The relationbetween φ-splitting and ψ-splitting with φ⊗ψ-splittingof the certain short exact sequence is obtained. We knowthat the admissible and splitting short exact sequencesplay important role in this talk. Also, we investigate therelation between φ- σwc virtual diagonals and thementioned notions. We obtain the relation between φ-Connes amenability ofA, φ-splitting of the certain shortexact sequence and φ- σwc virtual diagonals. Otherresults in this direction are also obtained.

کلیدواژه ها:

φ-σwc virtual diagonal ، φ-Connesamenability ، φ-splitting ، dual Banach algebra ، short exactsequence