Irreducible semigroups with multiplicative spectral radius Original Research Article

Irreducible multiplicative semigroups of finite dimensional linear operators with some additional properties are studied. Each of the properties—submultiplicativity of the spectral radius, its multiplicativity, or is constancy, as well as a certain property called the Rota condition—implies that every member of such a semigroup is, except for a scalar coefficient, similar to the direct sum of an isometry and a nilpotent operator.