Browsing Waterloo Research by Author "Radjavi, Heydar"
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Hilbert space operators with compatible offdiagonal corners
Livshits, Leo; MacDonald, Gordon; Marcoux, Laurent W.; Radjavi, Heydar (Elsevier, 20180815)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 finitedimensional, we also obtain a complete characterization of ... 
Linear preservers of polynomial numerical hulls of matrices
Aghamollaei, Gh.; Marcoux, L.W.; Radjavi, H. (Elsevier, 20190815)Let Mn be the algebra of all n × n complex matrices, 1 ≤ k ≤ n − 1 be an integer, and φ : Mn −→ Mn be a linear operator. In this paper, it is shown that φ preserves the polynomial numerical hull of order k if and only if ... 
On selfadjoint extensions of semigroups of partial isometries
Bernik, Janez; Marcoux, Laurent W.; Popov, Alexey I.; Radjavi, Heydar (American Mathematical Society, 2016)Let S be a semigroup of partial isometries acting on a complex, infinite dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists ... 
Ranges of vector states on irreducible operator semigroups
Marcoux, L.W.; Omladič, M.; Popov, A.I.; Radjavi, H.; Yahaghi, B. (Springer, 2016)Let 𝜑 be a linear functional of rank one acting on an irreducible semigroup S of operators on a finite or infinitedimensional Hilbert space. It is a wellknown and simple fact that the range of 𝜑 cannot be a singleton. ... 
Reducibility of operator semigroups and values of vector states
Marcoux, L.W.; Radjavi, H.; Yahaghi, B.R. (Springer, 20170801)Let S be a multiplicative semigroup of bounded linear operators on a complex Hilbert space H, and let Ω be the range of a vector state on S so that Ω = {⟨Sξ, ξ⟩ : S ∈ S} for some fixed unit vector ξ ∈ H. We study the ... 
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 finitedimensional 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 ...