Browsing University of Waterloo by Author "Radjavi, Heydar"
Now showing items 1-16 of 16
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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 ... -
Around the closure of the set of commutators of idempotents in B(H): Biquasitriangularity and factorisation
Marcoux, Laurent; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 2023-04-15)In this paper, we continue our study of the norm-closure of the set CEof bounded linear operators acting on a complex, infinite-dimensional, separable Hilbert space Hwhich may be expressed as the commutator of two idempotent ... -
Dispersing representations of semi-simple subalgebras of complex matrices
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 2022-06-01)In this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semi-simple 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 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 ... -
Linear preservers of polynomial numerical hulls of matrices
Aghamollaei, Gh.; Marcoux, L.W.; Radjavi, H. (Elsevier, 2019-08-15)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, 2021-07-15)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 off-diagonal corners
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Polish Academy of Sciences, 2020-05-25)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, self-adjoint algebras of complex n x n matrices that are simultaneously unitarily similar to algebras in which every member has a scalar diagonal. -
OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang (Elsevier, 2020-12-15)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 ⊥A|ran P is said to be an off-diagonal 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 infinite-dimensional Hilbert space. It is a well-known 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, 2017-08-01)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 finite-dimensional 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 ...