Algebraic operators, partial isometries, and wild problems. (English) Zbl 0941.47034
A notion of a wild \(*\)-algebra is applied to the study of certain classes of linear operators on a Hilbert space – algebraic operators, partial isometries, \(n\)-centered operators (intermediate between centered and weakly centered ones), and also to families of operators satisfying some relations. A \(*\)-algebraic version of the Morita equivalence and localization are used to prove the wildness of the unitary classification problems for algebraic partial isometries, \(n\)-centered partial isometries, pairs of self-adjoint operators connected by braid group relations.
Reviewer: A.N.Kochubei (Kiev)
MSC:
47C10 | Linear operators in \({}^*\)-algebras |
47A62 | Equations involving linear operators, with operator unknowns |
47A67 | Representation theory of linear operators |
47L99 | Linear spaces and algebras of operators |