On supermatrix idempotent operator semigroups Original Research Article

One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, the first giving rise to additional non-exponential solutions to the initial Cauchy problem. The corresponding functional equation and analog of resolvent are found. Differential and functional equations for idempotent (super)operators are derived for their general t power-type dependence.