On a Class of C-Algebras Generated by a Countable Family of Partial Isometries

摘要

The paper investigates the properties of an operator T_ψ on the Hilbert space ι~2(Z), which are induced by the mapping ψ of the set Z into itself. It is shown if the mapping ψ is such that every preimage has finite, but not equipotentionally bounded cardinality, then the operator T_ψ allows a closure and can be represented as a countable sum of partial isometries. The C* -algebras μ_ ψ P_ψ and U_ψ associated with given mappings and generated by the mentioned partial isometries are considered. Some properties of these algebras and some relations between them are given.