A remark on analytic subalgebras in von Neumann algebras (Q1813278)

Let \(M\) be a von Neumann algebra, \(\{\alpha_ t\}_{t\in\mathbb{R}}\) a \(\sigma\)-weakly continuous one-parameter group of \(*\)-automorphisms of \(M\). The analytic subalgebra \(H^ \infty(\alpha)\) of \(M\) is defined by \[ H^ \infty(\alpha)=\{x\in M:\;\text{Sp}_ \alpha(x)\subset[0,\infty)\}, \] where \(\text{Sp}_ \alpha(x)\) is the Arveson spectrum of \(x\). The aim of the paper under review is to investigate the structure of \(H^ \infty(\alpha)\) (invariant subspaces, the distance formula).