Normalisers of CSL algebras I. Todorov 47L3547L0546A32normalisersnest algebrasCSL algebras A coordinate description of the normalisers of CSL algebras is provided. It is shown that the linear span of the normalisers of a continuous nest algebra $\mathcal{A}$, which lie in $\mathcal{A}$, is ultraweakly dense in $\mathcal{A}$. It is proved that, within the classes of continuous nest algebras and totally atomic CSL algebras, the normaliser semigroup determines the algebra up to adjoint. A complete description of the relation between two nest algebras with the same normalisers is given. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2628 10.1512/iumj.2004.53.2628 en Indiana Univ. Math. J. 53 (2004) 1013 - 1036 state-of-the-art mathematics http://iumj.org/access/