Let E, F be exact operator spaces (for example subspaces of the C *-algebra K(H) of all the compact operators on an infinite dimensional Hilbert space H). We study a class of bounded linear maps u: E → F * which we call tracially bounded. In particular, we prove that every completely bounded (in short c.b.) map u: E → F * factors boundedly through a Hilbert space. This is used to show that the ...

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

We prove the following statements about bounded linear operators on a separable, complex Hilbert space: (1) Every normal operator N that is similar to a Hilbert-Schmidt perturbation of a diagonal operator D is unitarily equivalent to a Hilbert-Schmidt perturbation of D; (2) For every normal operator A', diagonal operator D and bounded operator X, the Hilbert-Schmidt norms (finite or infinite) o...

Assuming the continuum hypothesis, we show that the Calkin algebra has 2 ℵ 1 outer automorphisms. Let H be a separable infinite dimensional Hilbert space, let L(H) be the algebra of bounded operators on H, let K(H) be the algebra of compact operators on H, and let Q = L(H)/K(H) be the Calkin algebra. A long-standing problem asks whether every automorphism of Q is inner, that is, of the form x →...

Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are typically entangled. In contrast, here, we study the problem of performing coding in a high-dimensional Hilbert space, where the classes are expected to be m...

Using Toruńczyk’s charaterization theorem, we show that the space CB(X,Y ) of bounded continuous mappings from X into Y is a topological manifold modelled on the Hilbert space of weight 20 , with respect to the topology of uniform convergence, under the following three assumptions: (1) X is a noncompact, separable and metrizable space, (2) Y is a complete metric space which is an ANRU (ANR in u...

Let H be a separable real Hilbert space and let F = (Ft)t∈[0,T ] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T ] on a probability space (Ω,F ,P). We prove that if E is a UMD Banach space, 1 ≤ p < ∞, and F ∈ D(Ω;E) is FT -measurable, then F = E(F ) + ∫ T 0 PF(DF ) dWH , where D is the Malliavin derivative of F and PF is the projection onto the F-adapted ...

Let F be a separable Banach space, and let (X, Y ) be a random pair taking values in F×R. Motivated by a broad range of potential applications, we investigate rates of convergence of the k-nearest neighbor estimate rn(x) of the regression function r(x) = E[Y |X = x], based on n independent copies of the pair (X, Y ). Using compact embedding theory, we present explicit and general finite sample ...

The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other N−m qudits. We examine the entanglement in this mixed space of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than N/3...

Irreducible representations of B()i), with )i a not necessarily separable Hubert space, are constructed and analyzed along the lines of a similar study of Reid for separable Hubert spaces. Here we construct and study certain representations of B(M), the algebra of bounded operators on the Hubert space M. These have been studied previously by Calkin [4] for separable Hilbert spaces and in the ge...