Zobrazeno 1 - 10
of 271
pro vyhledávání: '"DAVIDSON, KENNETH R."'
Autor:
Davidson, Kenneth R.
Let $\mathcal{M}$ and $\mathcal{N}$ be nests on separable Hilbert space. If the two nest algebras are distance less than 1 ($d(\mathcal{T}(\mathcal{M}),\mathcal{T}(\mathcal{N})) < 1$), then the nests are distance less than 1 ($d(\mathcal{M},\mathcal{
Externí odkaz:
http://arxiv.org/abs/2408.03317
Autor:
Aubrun, Guillaume, Davidson, Kenneth R., Müller-Hermes, Alexander, Paulsen, Vern I., Rahaman, Mizanur
Given an operator system $\mathcal{S}$, we define the parameters $r_k(\mathcal{S})$ (resp. $d_k(\mathcal{S})$) defined as the maximal value of the completely bounded norm of a unital $k$-positive map from an arbitrary operator system into $\mathcal{S
Externí odkaz:
http://arxiv.org/abs/2401.12352
Autor:
Davidson, Kenneth R., Hartz, Michael
Let $S$ be an operator system sitting in its C*-envelope $C^*_{\mathrm{min}}(S)$. Starting with a pure state on $S$, let $F$ be the face of state extensions to $C^*_{\mathrm{min}}(S)$. The dilation theorem of Davidson-Kennedy shows that the GNS repre
Externí odkaz:
http://arxiv.org/abs/2308.04919
Publikováno v:
Annales Henri Poincar\'e (2023)
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert spaces, and litt
Externí odkaz:
http://arxiv.org/abs/2207.02510
Publikováno v:
Linear Algebra and its Applications (2023)
Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is re
Externí odkaz:
http://arxiv.org/abs/2204.08819
Autor:
Davidson, Kenneth R., Passer, Benjamin
Publikováno v:
Int. Math. Res. Not. IMRN 7 (2022), 5037-5070
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates the C*-env
Externí odkaz:
http://arxiv.org/abs/2005.11582
Autor:
Davidson, Kenneth R., Hartz, Michael
We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, to the Drury-Arves
Externí odkaz:
http://arxiv.org/abs/2003.14341
Autor:
Davidson, Kenneth R., Kennedy, Matthew
We introduce a new and extensive theory of noncommutative convexity along with a corresponding theory of noncommutative functions. We establish noncommutative analogues of the fundamental results from classical convexity theory, and apply these ideas
Externí odkaz:
http://arxiv.org/abs/1905.08436