Browsing Mathematics (Faculty of) by Author "Marcoux, Laurent"

Abelian, amenable operator algebras are similar to C∗ -algebras

Marcoux, Laurent W.; Popov, Alexey I. (Duke University Press, 2016-12)

Suppose that H is a complex Hilbert space and that ℬ(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C∗-algebra. We do this by showing that if 𝒜⊆ℬ(H) is ...

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 ...

Compact ideals and rigidity of representations for amenable operator algebras

Clouâtre, Raphaël; Marcoux, Laurent W. (Polish Academy of Sciences, 2019)

We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison’s conjecture on completely bounded homomorphisms ...

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 ...

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 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 ...

OPERATORS WHICH ARE POLYNOMIALLY ISOMETRIC TO A NORMAL OPERATOR

Marcoux, Laurent W.; Zhang, Yuanhang (American Mathematical Society, 2020-01-15)

Let H be a complex, separable Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. Given a unitarily-invariant norm k · ku on B(H) and two linear operators A and B in B(H), we shall say ...

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 ...

Residual finite dimensionality and representations of amenable operator algebras

Clouâtre, Raphaël; Marcoux, Laurent W. (Elsevier, 2019-04-15)

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable ...

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 ...