101,407 research outputs found
A characterisation of Wigner-Yanase skew information among statistically monotone metrics
No full textLet M-n = M-n(C) be the space of n x n complex matrices endowed with the Hilbert-Schmidt scalar product, let S-n be the unit sphere of M-n and let D-n subset of M-n be the space of strictly positive density matrices. We show that the scalar product over D-n introduced by Gibilisco and Isola(3) (that is the scalar product induced by the map D-n There Exists rho --> rootrho is an element of S-n) coincides with the Wigner-Yanase monotone metric
Spectral triples on irreversible C*-dynamical systems
No full textGiven a spectral triple on a C*-algebra together with a unital injective endomorphism α, the problem of defining a suitable crossed product C*-algebra endowed with a spectral triple is addressed. The proposed construction is mainly based on the works of Cuntz and [A. Hawkins, A. Skalski, S. White and J. Zacharias, On spectral triples on crossed products arising from equicontinuous actions, Math. Scand. 113(2) (2013) 262-291], and on our previous papers [V. Aiello, D. Guido and T. Isola, Spectral triples for noncommutative solenoidal spaces from self-coverings, J. Math. Anal. Appl. 448(2) (2017) 1378-1412; V. Aiello, D. Guido and T. Isola, A spectral triple for a solenoid based on the Sierpinski gasket, SIGMA Symmetry Integrability Geom. Methods Appl. 17(20) (2021) 21]. The embedding of α(A) in can be considered as the dual form of a covering projection between noncommutative spaces. A main assumption is the expansiveness of the endomorphism, which takes the form of the local isometricity of the covering projection, and is expressed via the compatibility of the Lip-norms on and α(A)
An asymptotic dimension for metric spaces, and the 0-th Novikov-Shubin invariant
No full textA nonnegative number d(infinity), called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and is invariant under rough isometries. It is then shown that for a class of open manifolds with bounded geometry the asymptotic dimension coincides with the 0-th Novikov-Shubin number alpha(0) defined in a previous paper [D. Guido, T. Isola, J. Funct. Analysis, 176 (2000)]. Thus the dimensional interpretation of alpha(0) given in the mentioned paper in the framework of noncommutative geometry is established on metrics grounds. Since the asymptotic dimension of a covering manifold coincides with the polynomial growth of its covering group, the stated equality generalises to open manifolds a result by Varopoulos
How to distinguish quantum covariances using uncertainty relations
No full textAbstractTo each operator monotone function it is possible to associate a quantum version of the classical covariance. We show that: i) only for regular quantum covariances one can prove non-trivial uncertainty relations; ii) the usual quantum covariance gives the best inequalities in this setting
Uncertainty principle for Wigner Yanase Dyson information in semifinite von Neumann algebras
No full textIn Ref. 9, Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty principle in the semifinite case
An inequality related to uncertainty principle in von Neumann algebras
No full textRecently Kosaki proved an inequality for matrices that can be seen as a kind of new uncertainty principle. Independently, the same result was proved by Yanagi et al. The new bound is given in terms of Wigner-Yanase-Dyson informations. Kosaki himself asked if this inequality can be proved in the setting of von Neumann algebras. In this paper we provide a positive answer to that question and moreover we show how the inequality can be generalized to an arbitrary operator monotone function
Singular Traces on Semifinite von Neumann Algebras
No full textSingular traces are constructed on a general semifinite von Neumann algebra, thus generalizing the result of Dixmier (C.R. Acad. Sci. Paris 262, 1966.) Moreover our technique produces singular traces on type II1 factors. Such traces, though vanishing on all bounded operators, are non trivial on the *-algebra of affiliated unbounded operators. On a semifinite factor, we show that all traces are given by a dilation invariant functional on the cone of positive decreasing functions on [0, infinity), and we prove that the existence of a singular trace which is non trivial on a given operator is equivalent to an eccentricity condition on the singular values function, a result which generalizes the theorem given in (S. Albeverio, D. Guide, A. Ponosov, and S. Scarlatti, J. Funct. Anal., to appear.) for B(H). (C) 1995 Academic Press, Inc
On the characterisation of paired monotone metrics
No full textMonotone metrics, Wigner-Yanase-Dyson information,
On a refinement of Heisenberg uncertainty relations by means of quantum Fisher information
No full textFisher information and Stam inequality on a finite group
No full textWe prove a discrete version of the Stam inequality for random variables taking values on a finite group
- …
