The paper under review sums up the main results investigated over the past 40 years about single elements of operator algebras. An element \(s\) of an (abstract) algebra \(\mathcal A\) is a single element of \(\mathcal A\) if \(asb=0\) and \(a,b\in {\mathcal A}\) implies that \(as=\) or \(sa=0\). The notion of ‘single element’ was first used in the operator theory by J. R. Ringrose [Am. J. Math. 83, 463–478 (1961; Zbl 0100.11602)]. The author points out that single elements have been used to study reflexive, generally non-selfadjoint operator algebras and lists some interesting open problems concerning single elements. The article may be used as a guide for further reading.
For the entire collection see [Zbl 1012.00041].