Browsing Pure Mathematics by Type "Article"
Now showing items 1-20 of 23
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Abelian, amenable operator algebras are similar to C∗ -algebras
(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
(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
(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 ... -
Compressions of Compact Tuples
(Elsevier, 2019-03-01)We study the matrix range of a tuple of compact operators on a Hilbert space and examine the notions of minimal, nonsingular, and fully compressed tuples. In this pursuit, we refine previous results by characterizing ... -
Dimensional dependence of the Stokes-Einstein relation and its violation
(American Institute of Physics, 2013-10-28)We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical ... -
Dispersing representations of semi-simple subalgebras of complex matrices
(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 ... -
Existence and uniqueness of weak homotopy moment maps
(Elsevier, 2018-09-01)We show that the classical results on the existence and uniqueness of moment maps in symplectic geometry generalize directly to weak homotopy moment maps in multisymplectic geometry. In particular, we show that their ... -
Geometrical Frustration and Static Correlations in a Simple Glass Former
(American Physical Society, 2012-01-18)We study the geometrical frustration scenario of glass formation for simple hard-sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding ... -
Geometrical frustration and static correlations in hard-sphere glass formers
(American Institute of Physics, 2013-03-28)We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated ... -
Hilbert space operators with compatible off-diagonal corners
(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
(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 ... -
A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences
(Elsevier, 2019-01-01)In 1927, Artin conjectured that any integer other than −1 or a perfect square generates the multiplicative group (Z/pZ)× for infinitely many p. In 2000, Moree and Stevenhagen considered a two-variable version of this ... -
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
(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
(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)
(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 fixed points of self maps of the free ball
(Elsevier, 2018-07-01)In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ... -
On selfadjoint extensions of semigroups of partial isometries
(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
(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
(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
(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 ...