Boolean algebras of projections and algebras of spectral operators. (Q1880027)

This paper deals with \(C^\ast\) and \(W^\ast\) (\(C^\ast\)-algebras that are dual spaces) subalgebras of \({\mathcal L}(X)\), the space of operators on a Banach space \(X\). Let BWO and BSO denote the strongest topologies coinciding with the weak and strong topologies on bounded subsets of \({\mathcal L}(X)\). Suppose that \(X\) has no isomorphic copy of \(c_0\). An interesting result from this paper states that for a bounded Boolean algebra of Hermitian projections \({\mathcal E} \subset {\mathcal L}(X)\), the weakly closed algebra generated by it is a \(W^\ast\)-algebra and any faithful representation of it as a von Neumann algebra on a Hilbert space is bicontinuous with respect to the BWO and BSO topologies.