198 citations · 1.1k across the 43 of their papers we have counts for
24 papers · 1 filter
A Note on Twisted Crossed Products and Spectral Triples
P. Antonini, D. Guido, T. Isola +1
Starting with a spectral triple on a unital -algebra with an action of a discrete group , if the action is uniformly bounded (in a Lipschitz sense) a spectral triple…
A noncommutative Sierpinski Gasket
Fabio Cipriani, Daniele Guido, Tommaso Isola +1
A quantized version of the Sierpinski gasket is proposed, on purely topological grounds, as a -algebra with a suitable form of self-similarity. Several pr…
Spectral triples on irreversible -dynamical systems
Valeriano Aiello, Daniele Guido, Tommaso Isola
Given a spectral triple on a -algebra together with a unital injective endomorphism , the problem of defining a suitable crossed product -algebra endowed…
A Spectral Triple for a Solenoid Based on the Sierpinski Gasket
Valeriano Aiello, Daniele Guido, Tommaso Isola
The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical fea…
Spectral triples for noncommutative solenoidal spaces from self-coverings
Valeriano Aiello, Daniele Guido, Tommaso Isola
Examples of noncommutative self-coverings are described, and spectral triples on the base space are extended to spectral triples on the inductive family of coverings, in such a way…
Spectral triples for nested fractals
Daniele Guido, Tommaso Isola
It is shown that, for nested fractals [T.Lindstrom, Mem. Amer. Math. Soc. 420, 1990], the main structural data, such as the Hausdorff dimension and measure, the geodesic distance (…
A Gromov-Hausdorff Distance between von Neumann Algebras and an Application to Free Quantum Fields
D. Guido, N. Marotta, G. Morsella +1
A distance between von Neumann algebras is introduced, depending on a further norm inducing the -topology on bounded sets. Such notion is related both with the Gromov-Hausdorf…
Zeta functions for infinite graphs and functional equations
Daniele Guido, Tommaso Isola
The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is dis…
Spectral triples for the Sierpinski Gasket
F. Cipriani, D. Guido, T. Isola +1
We construct a family of spectral triples for the Sierpinski Gasket . For suitable values of the parameters, we determine the dimensional spectrum and recover the Hausdorff meas…
Modular theory for the von Neumann algebras of Local Quantum Physics
Daniele Guido
In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be…
Bose Einstein condensation on inhomogeneous amenable graphs
Francesco Fidaleo, Daniele Guido, Tommaso Isola
We investigate the Bose-Einstein Condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Ham…
Ihara's zeta function for periodic graphs and its approximation in the amenable case
Daniele Guido, Tommaso Isola, Michel L. Lapidus
In this paper, we give a more direct proof of the results by Clair and Mokhtari-Sharghi on the zeta functions of periodic graphs. In particular, using appropriate operator-algebrai…
A trace on fractal graphs and the Ihara zeta function
Daniele Guido, Tommaso Isola, Michel L. Lapidus
Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions of finite graphs, by Sunada, Hashimoto, Bass, Stark and Terras, Mizuno and Sato…
Ihara zeta functions for periodic simple graphs
Daniele Guido, Tommaso Isola, Michel L. Lapidus
The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the a…
The problem of completeness for Gromov-Hausdorff metrics on C*-algebras
Daniele Guido, Tommaso Isola
It is proved that the family of equivalence classes of Lip-normed C*-algebras introduced by M. Rieffel, up to isomorphisms preserving the Lip-seminorm, is not complete w.r.t. the m…
Dimensions and spectral triples for fractals in R^N
Daniele Guido, Tommaso Isola
Two spectral triples are introduced for a class of fractals in R^n. The definitions of noncommutative Hausdorff dimension and noncommutative tangential dimensions, as well as the c…
On the domain of singular traces
Daniele Guido, Tommaso Isola
The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of som…
Dimensions and singular traces for spectral triples, with applications to fractals
Daniele Guido, Tommaso Isola
Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit. When…
Fractals in Noncommutative Geometry
Daniele Guido, Tommaso Isola
To any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has n…
Natural Energy Bounds in Quantum Thermodynamics
Daniele Guido, Roberto Longo
Given a stationary state for a noncommutative flow, we study a boundedness condition, depending on a positive parameter beta, which is weaker than the KMS equilibrium condition at…
Inclusions of second quantization algebras
Franca Figliolini, Daniele Guido
In this note we study inclusions of second quantization algebras, namely inclusions of von Neumann algebras on the Fock space of a separable complex Hilbert space H, generated by t…
Representations of Direct Product of Matrix Algebras
Daniele Guido, Lars Tuset
Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducibl…
Singular traces, dimensions, and Novikov-Shubin invariants
Daniele Guido, Tommaso Isola
In Alain Connes noncommutative geometry, the question of the existence of a non-trivial integral can be described in terms of the singular traceability of the compact operator |D|^…
Noncommutative Riemann integration and and Novikov-Shubin invariants for open manifolds
Daniele Guido, Tommaso Isola
Given a C*-algebra A with a semicontinuous semifinite trace tau acting on the Hilbert space H, we define the family R of bounded Riemann measurable elements w.r.t. tau as a suitabl…