A canonical trace associated with certain spectral triples.
A convenient setting for differential geometry and global analysis II
A convexity theorem for Poisson actions of compact Lie groups
A correction of two papers concerning Hilbert manifolds
A de Rham theorem in the context of noncommutative geometry.
A Direct Approach to the Determination of Gaussian and Scalar Curvature Functions.
A Free Convenient Vector Space for Holomorphic Spaces.
A general approximation theorem for Hilbert cube manifolds
A general Fredholm theory I: a splicing-based differential geometry
A general topology approach to the study of differentiability of convex functions in Banach spaces
A generalization of Steenrod’s approximation theorem
In this paper we aim for a generalization of the Steenrod Approximation Theorem from [16, Section 6.7], concerning a smoothing procedure for sections in smooth locally trivial bundles. The generalization is that we consider locally trivial smooth bundles with a possibly infinite-dimensional typical fibre. The main result states that a continuous section in a smooth locally trivial bundles can always be smoothed out in a very controlled way (in terms of the graph topology on spaces of continuous...
A generalized global differential calculus. II. Application to invariance under a Lie group
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A global differentiability result for solutions of nonlinear elliptic problems with controlled growths
Let be a bounded open subset of , . In we deduce the global differentiability result for the solutions of the Dirichlet problem with controlled growth and nonlinearity . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
A Hahn-Banach extension theorem for analytic mappings
A Kähler structure on moduli space of isometric maps of a circle into Euclidean space.
A new construction of characteristic classes for noncommutative algebraic principal bundles
We propose a new construction of characteristic classes for noncommutative algebraic principal bundles (Hopf-Galois extensions) with values in Hochschild and cyclic homology.
A new proof of Szabó's theorem on the Riemann-metrizability of Berwald manifolds.
A noncommutative 2-sphere generated by the quantum complex plane
S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions...
A nonsmooth exponential
Let ℳ be a type II₁ von Neumann algebra, τ a trace in ℳ, and L²(ℳ,τ) the GNS Hilbert space of τ. If L²(ℳ,τ)₊ is the completion of the set of selfadjoint elements, then each element ξ ∈ L²(ℳ,τ)₊ gives rise to a selfadjoint unbounded operator on L²(ℳ,τ). In this note we show that the exponential exp: L²(ℳ,τ)₊ → L²(ℳ,τ), , is continuous but not differentiable. The same holds for the Cayley transform . We also show that the unitary group with the strong operator topology is not an embedded submanifold...