Tillmann [Tillmann H. G., <i>Zur Eindeutigkeit der Losungen der quanten mechanischen vertauschungrelationen</i>, Acta Sci. Math. (Szeged) 24 (1963), 258-270] proved that every operator $A$ which fulfils the canonical commutation relation $A^{*}A - AA^{*} = Id$ is an orthogonal sum of canonical creation operators. We extend this result for operators which fulfil generalized commutation relations $A^{*}A - AA^{*}= E^2,\text{ where }EA = AE.$ In addition, some inequalities which are helpful in describing analytic vectors of operators $A^{*}A$, where $A$ fulfils the generalized commutation relation, are established.
