Analysis seminar

Heydar Radjavi, Department of Pure Mathematics, University of Waterloo

“Simultaneous Versions of Wielandt’s Positivity Theorem”

The classical Wielandt Theorem is about ”positivisation” of a matrix: If an indecomposable matrix A and and its modulus |A| have the same spectral radius, then, after a diagonal similarity, A is just a scalar multiple of |A|. Here |A| is the matrix whose entries are the moduli of those of A; and “indecomposable” means that no nontrivial subset of the basic vectors spans an invariant subspace for (the operator whose matrix relative to this basis is) A. In joint work with Gordon Macdonald, we present extensions of this result to certain semigroups of operators in finite and infinite dimensions.