an:07040714
Zbl 1419.46031
Hayati, B.
Connes-amenability of \(WAP(\mathfrak B^*)^*\)
EN
Bull. Iran. Math. Soc. 44, No. 4, 1069-1077 (2018).
00430159
2018
j
46H20 46H25 47L10
amenability; Connes-amenability; multiplier Banach algebra; weakly almost periodic functions
Summary: For a Banach algebra \(\mathfrak B\), the set of weakly almost periodic functions on \(\mathfrak B\) is denoted by \(WAP(\mathfrak B^*)\). It is known that amenability of \(\mathfrak B\) yields Connes-amenability of \(WAP(\mathfrak B^*)^*\). The converse is not generally true though. We prove that under certain assumptions, \(\mathfrak B\) is amenable if and only if \(WAP(\mathfrak B^*)^*\) is Connes-amenable. As a result, we show that for a reflexive Banach space \(E\) with the approximation property, \(K(E)\) is amenable if and only if \(WAP(K(E)^*)^*\) is Connes-amenable.