Matjaz Omladic - Irreducible semigroups with multiplicative spectral radius

Irreducible multiplicative semigroups of complex matrices with some additional properties are studied. Each of the properties: submultiplicativity of the spectral radius, its multiplicativity, or its 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.