Zobrazeno 1 - 10
of 75
pro vyhledávání: '"Martin, Robert T. W."'
A realization is a triple, $(A,b,c)$, consisting of a $d-$tuple, $A= (A =_1, \cdots, A_d )$, $d\in \mathbb{N}$, of bounded linear operators on a separable, complex Hilbert space, $\mathcal{H}$, and vectors $b,c \in \mathcal{H}$. Any such realization
Externí odkaz:
http://arxiv.org/abs/2404.16675
We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their reproduci
Externí odkaz:
http://arxiv.org/abs/2312.01961
Autor:
Martin, Robert T. W., Shamovich, Eli
We apply realization theory of non-commutative rational multipliers of the Fock space, or free Hardy space of square--summable power series in several non-commuting variables to the convex analysis of states on the Cuntz algebra. We show, in particul
Externí odkaz:
http://arxiv.org/abs/2307.00508
Autor:
Martin, Robert T. W.
Let $A$ be a bounded, injective and self-adjoint linear operator on a complex separable Hilbert space. We prove that there is a pure isometry, $V$, so that $AV>0$ and $A$ is Hankel with respect to $V$, i.e. $V^*A = AV$, if and only if $A$ is not inve
Externí odkaz:
http://arxiv.org/abs/2205.15925
Autor:
Jury, Michael T., Martin, Robert T. W.
In the classical Hardy space theory of square-summable Taylor series in the complex unit disk there is a circle of ideas connecting Szeg\"o's theorem, factorization of positive semi-definite Toeplitz operators, non-extreme points of the convex set of
Externí odkaz:
http://arxiv.org/abs/2204.05016
We characterize the non-commutative Aleksandrov--Clark measures and the minimal realization formulas of contractive and, in particular, isometric non-commutative rational multipliers of the Fock space. Here, the full Fock space over $\mathbb{C} ^d$ i
Externí odkaz:
http://arxiv.org/abs/2201.08045
We extend results on analytic complex measures on the complex unit circle to a non-commutative multivariate setting. Identifying continuous linear functionals on a certain self-adjoint subspace of the Cuntz--Toeplitz $C^*-$algebra, the free disk oper
Externí odkaz:
http://arxiv.org/abs/2201.07393
Autor:
Jury, Michael T., Martin, Robert T. W.
We examine densely defined (but possibly unbounded) multiplication operators in Hilbert function spaces possessing a complete Nevanlinna-Pick (CNP) kernel. For such a densely defined operator $T$, the domains of $T$ and $T^*$ are reproducing kernel H
Externí odkaz:
http://arxiv.org/abs/2108.04383
Publikováno v:
J. Math. Anal. Appl. Volume 514, Issue 1, 1 October 2022, 126275
The theory of finite-rank perturbations allows for the determination of spectral information for broad classes of operators using the tools of analytic function theory. In this work, finite-rank perturbations are applied to powers of the derivative o
Externí odkaz:
http://arxiv.org/abs/2106.04500
The main objects of study in this paper are those functionals that are analytic in the sense that they annihilate the non-commutative disc algebra. In the classical univariate case, a theorem of F. and M. Riesz implies that such functionals must be g
Externí odkaz:
http://arxiv.org/abs/2104.02130