60 citations · 156 across the 15 of their papers we have counts for
16 papers
Quantum differentials of Spectral triples, Dirichlet spaces and discrete groups
Fabio E. G. Cipriani, Jean-Luc Sauvageot
We study natural conditions on essentially discrete spectral triples by which the quantum differential belongs to the ideal generated by the unit length . We also s…
Measurability, Spectral Densities and Hypertracesin Noncommutative Geometry
Fabio E. G. Cipriani, Jean-Luc Sauvageot
We introduce, in the dual Macaev ideal of compact operators of a Hilbert space, the spectral weight of a positive, self-adjoint operator having discrete spectrum away fr…
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…
KMS Dirichlet forms, coercivity and super-bounded Markovian semigroups on von Neumann algebras
Fabio E. G. Cipriani, Boguslaw Zegarlinski
We introduce a construction of Dirichlet forms on von Neumann algebras M associated to any eigenvalue of the Araki modular Hamiltonian of a faithful normal non tracial state, provi…
The emergence of Noncommutative Potential Theory
Fabio E. G. Cipriani
We review origins and developments of Noncommutative Potential theory as underpinned by the notion of energy form. Recent and new applications are shown to approximation properties…
On the eigenvalue counting function for Schrödinger operator: some upper bounds
Fabio E. G. Cipriani
The aim of this work is to provide an upper bound on the eigenvalues counting function of a Schödinger operator on corresponding to a…
Listening to the shape of a drum
Fabio E. G. Cipriani, J. -L. Sauvageot
The aim of this work is to link the quasiconformal geometry of a Euclidean domain to the spectral properties of its Dirichlet integral $\D$, through the algebra of multipliers…
Amenability and subexponential spectral growth rate of Dirichlet forms on von Neumann algebras
Fabio Cipriani, Jean-Luc Sauvageot
In this work we apply Noncommutative Potential Theory to prove (relative) amenability and the (relative) Haagerup Property of von Neumann algebras in terms of the spectral gr…
Negative type functions on groups with polynomial growth
Fabio Cipriani, Jean-Luc Sauvageot
The aim of this work is to show that on a locally compact, second countable, compactly generated group with polynomial growth and homogeneous dimension , there exist a con…
Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory
Fabio Cipriani, Uwe Franz, Anna Kula
Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show th…
Variations in noncommutative potential theory: finite energy states, potentials and multipliers
Fabio Cipriani, Jean-Luc Sauvageot
In this work we undertake an extension of various aspects of the potential theory of Dirichlet forms from locally compact spaces to noncommutative C*-algebras with trace. In partic…
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…
Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket
Fabio Cipriani, Daniele Guido, Tommaso Isola +1
We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can…
Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry
Fabio Cipriani, Jean-Luc Sauvageot
The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fr…
Hypercontractivity, Nash inequalities, and subordination for classes of nonlinear semigroups
Fabio Cipriani, Gabriele Grillo
A suitable notion of hypercontractivity for a nonlinear semigroup is shown to imply Gagliardo--Nirenberg inequalities for its generator , provided a subhomogeneity pro…
A remark on trace properties of K-cycles
Fabio Cipriani, Daniele Guido, Sergio Scarlatti
In this paper we discuss trace properties of -summable -cycles considered by A.Connes in [\rfr(Conn4)]. More precisely we give a proof of a trace theorem on the algebra $\A…