Some properties of clustering operators (Q1821327)

\textit{V. A. Malyshev} and \textit{R. A. Minlos} [Commun. Math. Phys. 82, 211- 216 (1981; Zbl 0505.47003)] considered a class of cluster operators acting on the space of finite unit-functions on an integer-valued lattice \(Z^{\upsilon}\). In this paper the author attempts to generalize their results to clustering operators on spaces of the type \(\ell_ 2({\mathfrak A})\) where \({\mathfrak A}\) is the set of all finite functions with natural values. No proofs are given in this paper.