Derivations as square roots of Dirichlet forms

By F. Cipriani, J. Sauvageot. 2003

165 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4540bc55ebdc855c7ac60c57ec3fd48c78f6e39c

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Noncommutative martingale deviation and Poincaré type inequalities with applications (2012, result): “Since compactly supported smooth functions are dense in the graph norm of A, the work of Cipriani and Sauvageot [12] shows that Condition (2) is automatically satisfied.”
A free stochastic partial differential equation (2010, unknown): “[9]) φt and ηα are completely positive contractions on M .”
Smooth Fourier multipliers on group von Neumann algebras (2010, background): “sume that the set of elements 6 JUNGE, MEI AND PARCET f∈ M such that the gradient Γ(f,f) = L1 − lim t→0 St(f∗f)+f∗f−St(f∗)f−f∗St(f) 2t exist in L1 —both for fand f∗— is weakly dense in M. We refer to [15, 67] for more information on gradients, or as Meyer’s calls them “carr´e du champs”. Under that ”
Dirichlet Forms on Noncommutative Spaces (2008, methodology): “in terms of representations of the maximal tensor product A ⊗max A ◦ . The content of this section is taken from [ CS1 ].”
Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance (2016, background): “A powerful non-commutative extension of this theory has been developed starting with the early work of Gross [31, 32], and continuing with [3, 15, 16, 18, 21, 29].”
Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces (2012, methodology): “We start from the notion of 1-forms based on energy as recently introduced by Cipriani and Sauvageot in [12, 13] and further studied in [35].”
L2-rigidity in von Neumann algebras (2009, methodology): “This equivalence is achieved in part by using Sauvageot’s results ([S1], [S3], [ CiS ]) which state that there is a bijective correspondence between densely defined real closable derivations into Hilbert bimodules and semigroups of unital, tracial completely positive maps.”