On the simplicial cohomology of Banach operator algebras (Q537714)

For a Banach algebra \(A\), a Banach \(A\)-bimodule \(E\) and a non-negative integer \(n\), let \(\mathcal{H}^n(A,E) = \{ 0 \}\) denote the \(n\)-th (bounded) Hochschild cohomology group of \(A\) with coefficients in \(E\). If \(\mathcal{H}^n(A,A') = \{ 0 \}\), where \(A'\) is the dual space of \(A\), we say that \(A\) is \textit{simplicially trivial}. The author first proves a general, very technical theorem that forces certain bounded cocycles to be coboundaries. He then applies it to establish the simplicial triviality of various algebras of bounded linear operators on particular Banach spaces.