Zobrazeno 1 - 10
of 137
pro vyhledávání: '"Isola, T"'
Publikováno v:
Journal of Geometry and Physics 180 (2022) 104640
Starting with a spectral triple on a unital $C^{*}$-algebra $A$ with an action of a discrete group $G$, if the action is uniformly bounded (in a Lipschitz sense) a spectral triple on the reduced crossed product $C^{*}$-algebra $A\rtimes_{r} G$ is con
Externí odkaz:
http://arxiv.org/abs/2110.05345
Publikováno v:
J. Funct. Anal., 266 (2014) 4809-4869
We construct a family of spectral triples for the Sierpinski Gasket $K$. For suitable values of the parameters, we determine the dimensional spectrum and recover the Hausdorff measure of $K$ in terms of the residue of the volume functional $a\to$ tr$
Externí odkaz:
http://arxiv.org/abs/1112.6401
Publikováno v:
Linear Algebra and its Applications, 430 (2009), 2225-2232
We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to Wigner-Yanase-Dyson skew inf
Externí odkaz:
http://arxiv.org/abs/0808.0468
Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$ det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j])) $$ gives a bound for the quantum generalized covariance in
Externí odkaz:
http://arxiv.org/abs/0706.0791
Heisenberg and Schr{\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$, in a state $\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not zero. In
Externí odkaz:
http://arxiv.org/abs/math-ph/0701062
Autor:
Gibilisco, P., Isola, T.
We show that an inequality recently proved by Kosaki and Yanagi-Furuichi-Kuriyama [arXiv:quant-ph/0501152] has a natural geometric interpretation in terms of monotone metrics associated to Wigner-Yanase-Dyson information. Moreover we give a counterex
Externí odkaz:
http://arxiv.org/abs/math-ph/0509046
Autor:
Gibilisco, P., Isola, T.
We study the statistical monotonicity of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data we are led to some conjectures about quantum alpha-geometries and Wigner-Y
Externí odkaz:
http://arxiv.org/abs/math-ph/0407007
Autor:
Gibilisco, P., Isola, T.
In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by Petz. All the
Externí odkaz:
http://arxiv.org/abs/math/0304170
Autor:
Gibilisco, P., Isola, T.
Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisatio
Externí odkaz:
http://arxiv.org/abs/math/0303059
A trace on the C^*-algebra A of quasi-local operators on an open manifold is described, based on the results in \cite{RoeOpen}. It allows a description `a la Novikov-Shubin \cite{NS2} of the low frequency behavior of the Laplace-Beltrami operator. Th
Externí odkaz:
http://arxiv.org/abs/dg-ga/9612015