We present a natural family of Hilbert function spaces on the d-dimensional complex unit ball and classify which them satisfy that subsets yield isometrically isomorphic subspaces if only there is an analytic automorphism taking one to other. also characterize pairs weighted Hardy disk are via composition operator by simple criterion their respective sequences weights.

If 0 < p < 1 we classify completely the linear operators T: Lp -X where X is a p-convex symmetric quasi-Banach function space. We also show that if T: LLo is a nonzero linear operator, then forp < q < 2 there is a subspace Z of Lp, isomorphic to Lq, such that the restriction of T to Z is an isomorphism. On the other hand, we show that if p < q < o, the Lorentz space L(p, q) is a quotient of Lp ...

We study the structure group of a canonical algebraic curvature tensor built from a symmetric bilinear form, and show that in most cases it coincides with the isometry group of the symmetric form from which it is built. Our main result is that the structure group of the direct sum of such canonical algebraic curvature tensors on a decomposable model space must permute the subspaces Vi on which ...

Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schrödinger operators are extended to allow singular potentials such as certain Lp-functions. The proof is based on accordingly adapted Carleman estimates. Applications include Wegner and initial length scale random control theory the controlled heat equation with generation term.

We discuss representations of the projective line over a ring R with 1 in a projective space over some (not necessarily commutative) field K. Such a representation is based upon a (K,R)-bimodule U . The points of the projective line over R are represented by certain subspaces of the projective space P(K,U ×U) that are isomorphic to one of their complements. In particular, distant points go over...

Let X 1 and X 2 be subspaces of quotients of R ⊕ OH and C ⊕ OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product X 1 ⊗ h X 2 into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of ℓq (equipped with...

We explore the existence of uniformly continuous sections for quotient maps. Using this approach we are able to give a number of new examples in the theory of the uniform structure of Banach spaces. We show for example that there are two non-isomorphic separable L1-subspaces of 1 which are uniformly homeomorphic. We also prove the existence of two coarsely homeomorphic Banach spaces (i.e. with ...

In this paper we introduce a new topological Ramsey space P whose elements are infinite ordered polyhedra. The corresponding familiy AP of finite approximations can be viewed as a class of finite structures. It turns out that the closure of AP under isomorphisms is the class KP of finite ordered polyhedra. Following [8], we show that KP is a Ramsey class. Then, we prove a universal property for...

To any graph G one can associate a toric variety X(PG), obtained as a blowup of projective space along coordinate subspaces corresponding to connected subgraphs of G. The polytope of this toric variety is the graph associahedron of G, a class of polytopes that includes the permutohedron, associahedron, and stellahedron. We show that the space X(PG) is isomorphic to a Hassett compactification of...