Lipschitz algebras and derivations. II: Exterior differentiation

DOI10.1006/jfan.2000.3637zbMath0979.46035arXivmath/9807096OpenAlexW2592646876MaRDI QIDQ1840771

Nikolai Weaver

Publication date: 22 July 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9807096

zbMATH Keywords

derivationsDirichlet spaceLipschitz algebrasexterior differentiation\(W^*\)-module\(W^*\)-derivation

Mathematics Subject Classification ID

(C^*)-modules (46L08) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

Related Items (46)

Lecture notes on differential calculus on \(\mathsf{RCD}\) spaces ⋮ On BV functions and essentially bounded divergence-measure fields in metric spaces ⋮ Infinitesimal structure of differentiability spaces, and metric differentiation ⋮ On Lipschitz vector fields and the Cauchy problem in homogeneous groups ⋮ Metric currents and Alberti representations ⋮ Differentiability and Poincaré-type inequalities in metric measure spaces ⋮ Three superposition principles: currents, continuity equations and curves of measures ⋮ Weak and strong convergence of derivations and stability of flows with respect to MGH convergence ⋮ Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions ⋮ Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications ⋮ On the differential structure of metric measure spaces and applications ⋮ Hölder classes via semigroups and Riesz transforms ⋮ Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces ⋮ Calculus and fine properties of functions of bounded variation on RCD spaces ⋮ Lie brackets of nonsmooth vector fields and commutation of their flows ⋮ Derivations as square roots of Dirichlet forms ⋮ Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces ⋮ Lecture notes on the DiPerna–Lions theory in abstract measure spaces ⋮ New differential operator and noncollapsed RCD spaces ⋮ Rigidity of derivations in the plane and in metric measure spaces ⋮ Rigidity of some functional inequalities on RCD spaces ⋮ An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature ⋮ The Poincaré inequality does not improve with blow-up ⋮ Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below ⋮ The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms ⋮ Local currents in metric spaces ⋮ On Cheeger and Sobolev differentials in metric measure spaces ⋮ Characterizations and extensions of Lipschitz-\(\alpha\) operators ⋮ Differential of metric valued Sobolev maps ⋮ SECOND-ORDER NONCOMMUTATIVE DIFFERENTIAL AND LIPSCHITZ STRUCTURES DEFINED BY A CLOSED SYMMETRIC OPERATOR ⋮ Rough traces of BV functions in metric measure spaces ⋮ Convergence of non-symmetric diffusion processes on RCD spaces ⋮ A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations ⋮ A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations ⋮ Infinitesimal hilbertianity of locally \(\mathrm{CAT}(\kappa)\)-spaces ⋮ Sierpinski-type fractals are differentiably trivial ⋮ Measurable metrics and Gaussian concentration ⋮ Approximation of partial differential equations on compact resistance spaces ⋮ The Serre-Swan theorem for normed modules ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ A differentiable structure for metric measure spaces ⋮ Point derivations and cohomologies of Lipschitz algebras ⋮ Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals ⋮ Weakly non-collapsed RCD spaces are strongly non-collapsed ⋮ Derivations and Alberti representations ⋮ The Lip-lip equality is stable under blow-up

Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The construction of Brownian motion on the Sierpinski carpet
• Dirichlet forms of fractals and products of random matrices
• Differential forms on Lipschitz manifolds
• Brownian motion on the Sierpinski gasket
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Dirichlet forms and analysis on Wiener space
• Analysis on graphs and noncommutative geometry
• Symmetric Markov processes
• Induced representations and Banach \(^*\)-algebraic bundles. With an appendix due to A. Douady and L. Dal Soglio-Herault
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Analysis on fractals, Laplacians on self-similar sets, noncommutative geometry and spectral dimensions
• LIP manifolds: from metric to Finslerian structure
• Modules with norms which take values in a \(C^*\)-algebra
• Definitions of quasiconformality
• Order completeness in Lipschitz algebras
• An introduction to analysis on Wiener space
• A Kähler structure on the moduli space of isometric maps of a circle into Euclidean space
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• A Saint-Venant type principle for Dirichlet forms on discontinuous media
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• Lipschitz algebras and derivations of von Neumann algebras
• Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Amenability and Weak Amenability for Beurling and Lipschitz Algebras
• Hardy Spaces of Harmonic Functions on Homogeneous Isotropic Trees
• Harmonic analysis of the de Rham complex on the sphere.
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Mesures associées à une forme de Dirichlet. Applications
• Elements of Lipschitz topology
• A harmonic calculus on the Sierpinski spaces
• Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
• Harmonic analysis of fractal measures induced by representations of a certain 𝐶*-algebra
• Stokes’ theorem for nonsmooth chains
• Large Deviations for Heat Kernels on Graphs
• Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
• An 𝑛-dimensional space that admits a Poincaré inequality but has no manifold points
• Nonatomic Lipschitz spaces
• Abstract covariant derivative
• Differential modules
• Inner Product Modules Over B ∗ -Algebras
• ON SUBMANIFOLDS OF CERTAIN FUNCTION SPACES

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