Now showing items 1-16 of 16


      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 ...

      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.

      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 A􀀀1 if Y = s􀀀1Xs and Y = s􀀀1X 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 ...


      University of Waterloo Library
      200 University Avenue West
      Waterloo, Ontario, Canada N2L 3G1
      519 888 4883

      All items in UWSpace are protected by copyright, with all rights reserved.

      DSpace software

      Service outages