Browsing Waterloo Research by Author "Livshits, Leo"
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ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS
Bernik, Janez; Livshits, Leo; MacDonald, Gordon W.; Marcoux, Laurent W.; Mastnak, Mitja; Radjavi, Heydar (American Mathematical Society, 2021-07-20)We study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly ... -
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 spatial version of Wedderburn’s Principal Theorem
Livshits, L.; MacDonald, G.W.; Marcoux, L.W.; Radjavi, H. (Taylor & Francis, 2015)In this article we verify that ‘Wedderburn’s Principal Theorem’ has a particularly pleasant spatial implementation in the case of cleft subalgebras of the algebra of all linear transformations on a finite-dimensional vector ... -
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 ...