Browsing University of Waterloo by Author "MacDonald, Gordon"

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Hilbert space operators with compatible off-diagonal corners

Livshits, Leo; MacDonald, Gordon; Marcoux, Laurent W.; Radjavi, Heydar (Elsevier, 2018-08-15)

Given a complex, separable Hilbert space H, we characterize those operators for which ‖PT(I−P)‖=‖(I−P)TP‖ for all orthogonal projections P on H. When H is finite-dimensional, we also obtain a complete characterization of ...
A note on the structure of matrix *-subalgebras with scalar diagonals

MacDonald, Gordon; Mastnak, Mitja; Omladic, Matjaz; Radjavi, Heydar (EleMath, 2021)

We characterize those unital, self-adjoint algebras of complex n x n matrices that are simultaneously unitarily similar to algebras in which every member has a scalar diagonal.
Universal bounds for positive matrix semigroups

Livshits, Leo; MacDonald, Gordon; Marcoux, Laurent; Radjavi, Heydar (Polish Academy of Sciences, 2016)

We show that any compact semigroup of positive n×n matrices is similar (via a positive diagonal similarity) to a semigroup bounded by n√. We give examples to show this bound is best possible. We also consider the effect ...