EXTENSION OF DERIVATIONS, AND CONNES-AMENABILITY OF THE ENVELOPING DUAL BANACH ALGEBRA

作者：Choi Yemon^*; Samei Ebrahim; Stokke Ross

来源：Mathematica Scandinavica, 2015, 117(2): 258-303.

If D : A -> Xis a derivation from a Banach algebra to a contractive, Banach A-bimodule, then one can equip X** with an A**-bimodule structure, such that the second transpose D** : A** -> X** is again a derivation. We prove an analogous extension result, where A** is replaced by F(A), the enveloping dual Banach algebra of A, and X** by an appropriate kind of universal, enveloping, normal dual bimodule of X.
Using this, we obtain some new characterizations of Connes-amenability of F(A). In particular we show that F(A) is Connes-amenable if and only if A admits a so-called WAP-virtual diagonal. We show that when A = L-1 (G), existence of a WAP-virtual diagonal is equivalent to the existence of a virtual diagonal in the usual sense. Our approach does not involve invariant means for G.

• 出版日期2015