Non-Hilbertian tangents to Hilbertian spaces

Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below

We show that in any infinitesimally Hilbertian CD∗(K,N)-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian CD∗(0, N)-spaces.

HOMOGENEOUS HILBERTIAN SUBSPACES OF NON-COMMUTATIVE Lp SPACES

December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...

Classification of Contractively Complemented Hilbertian Operator Spaces

We construct some separable infinite dimensional homogeneous Hilbertian operator spaces H ∞ and H m,L ∞ , which generalize the row and column spaces R and C (the case m = 0). We show that separable infinitedimensional Hilbertian JC∗-triples are completely isometric to an element of the set of (infinite) intersections of these spaces . This set includes the operator spaces R, C, R ∩ C, and the s...

‘non – Hilbertian’ Quantum Mechanics on the Finite

Abundance of Hilbertian Domains

We construct an abundance of Hilbertian domains: Let O be a countable separably Hilbertian domain with a qoutient eld K and let e 2 be an integer. Let L be an abelian extension of K such that ford(a) j a 2 G(L=K)g is unbounded, and let O L be the integral closure of O in L. Then, for almost all 2 G(K) e , each ring between O L and L K s () is separably Hilbertian.