Browsing University of Waterloo by Author "216d1867db484f0aa7f7b6c66ebec1fb"
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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, 20210720)We study the maximal algebraic degree of principal orthocompressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly ... 
Around the closure of the set of commutators of idempotents in B(H): Biquasitriangularity and factorisation
Marcoux, Laurent; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 20230415)In this paper, we continue our study of the normclosure of the set CEof bounded linear operators acting on a complex, infinitedimensional, separable Hilbert space Hwhich may be expressed as the commutator of two idempotent ... 
Dispersing representations of semisimple subalgebras of complex matrices
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 20220601)In this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semisimple subalgebras of the set Mn of n⇥n complex matrices, and P 2 M2n is a projection of rank n. We ... 
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 ... 
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
Cramer, Zachary; Marcoux, Laurent W.; Radjavi, Heydar (Elsevier, 20210715)An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all ... 
Normal operators with highly incompatible offdiagonal corners
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Polish Academy of Sciences, 20200525)Let H be a complex, separable Hilbert space, and B(H) denote the set of all bounded linear operators on H. Given an orthogonal projection P∈B(H) and an operator D∈B(H), we may write D=[D1D3D2D4] relative to the decomposition ... 
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, selfadjoint algebras of complex n x n matrices that are simultaneously unitarily similar to algebras in which every member has a scalar diagonal. 
OFFDIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 20201215)Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥Aran P is said to be an offdiagonal corner of A, and L ... 
On *similarity in C*algebras
Marcoux, Laurent; Radjavi, Heydar; Yahaghi, B.R. (Instytut Matematyczny, 2020)Two subsets X and Y of a unital C algebra A are said to be similar via s 2 A1 if Y = s1Xs and Y = s1X s. We show that this relation imposes a certain structure on the sets X and Y, and that under certain natural ... 
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 ... 
Triangular Operator Algebras and Simultaneous Triangularisation
Marcoux, Laurent; Radjavi, Heydar; Rosenthal, Peter (American Mathematical Society, 2023)We consider the question of whether every collection of compact operators that is contained in a triangular operator algebra (in the sense of Kadison and Singer) must be simultaneously triangularisable. The answer is shown ... 
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 ...