Period of an irreducible positive operator

Irreducible Positive Linear Maps on Operator Algebras

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...

Positive operator valued measures covariant with respect to an irreducible representation

Given an irreducible representation of a group G, we show that all the covariant positive operator valued measures based on G/Z, where Z is a central subgroup, are described by trace class, trace one positive operators.

Irreducible Representations of Operator Algebras

Irreducible and Periodic Positive Maps

We extend the notions of irreducibility and periodicity of a stochastic matrix to a unital positive linear map © on a finite-dimensional C∗algebra A and discuss the non-commutative version of the Perron-Frobenius theorem. For a completely positive linear map © with ©(a) = ∑ l Ll ∗aLl, we give conditions on the Ll’s equivalent to irreducibility or periodicity of ©. As an example, positive linear...

Irreducible canonical representations in positive characteristic

For X a curve over a field of positive characteristic, we investigate when the canonical representation of Aut(X) on H0(X , X) is irreducible. Any curve with an irreducible canonical representation must either be superspecial or ordinary. Having a small automorphism group is an obstruction to having irreducible canonical representation; with this motivation, the bulk of the paper is spent bound...