Let k be the reporducing kernel for a Hilbert space H(k) of nanlytic functions on Bd, the open unit ball in C, d ≥ 1. k is called a complete NP kernel, if k0 ≡ 1 and if 1 − 1/kλ(z) is positive definite on Bd × Bd. Let D be a separable Hilbert space, and consider H(k) ⊗ D ∼= H(k,D), and think of it as a space of D-valued H(k)-functions. A theorem of McCullough and Trent, [10], partially extends ...

We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space H we characterize the subspaces of L(R , H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge sym...

Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W−1 both satisfy a matrix reverse Hölder property introduced in [2], then the weighted Hilbert transform H : LW (R,H) → L 2 W (R,H) and also all weighted dyadic martingale transforms Tσ : LW (R,H)→ L 2 W (R,H) are bound...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

Let Z be a fixed separable operator space, X ⊂ Y general separable operator spaces, and T : X → Z a completely bounded map. Z is said to have the Complete Separable Extension Property (CSEP) if every such map admits a completely bounded extension to Y ; the Mixed Separable Extension Property (MSEP) if every such T admits a bounded extension to Y . Finally, Z is said to have the Complete Separab...

Recently the author [Proc. Amer. Math. Soc. 103(1988), 11291135] proved random versions of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] for continuous condensing random maps and nonexpansive random maps defined on a closed convex bounded subset in a separable Hilbert space. In this paper, we prove that it is still true for (more general) continuous 1-set-contractiv...

The Cramér–Wold theorem states that a Borel probability measure P on R is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how large a subset of these projections is really needed to determine P . We also consider extensions of our results to measures on a separable Hilbert space. As an application of these ideas, we derive ...

in this paper, we show that in each nite dimensional hilbert space, a frame of subspaces is an ultra bessel sequence of subspaces. we also show that every frame of subspaces in a nite dimensional hilbert space has frameness bound.

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized eigenvalue type expansions. Though there are formal similarities with earlier approaches to special cases of the problem, the paper differs e.g. from standar...