We give a necessary and sufficient condition for the second quantification operator Γ(h) of a bounded operator h on L2 (R+), or for its differential second quantification operator λ(h), to have a representation as a quantum stochastic integral. This condition is exactly that h writes as the sum of a Hilbert-Schmidt operator and a multiplication operator. We then explore several extensions of th...

The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young's and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young's inequalities are promoted, the operator version and the Hilbert-Schmidt form ...

Abstract. In this paper we obtain a necessary and sufficient condition for the canonical solution operator to ∂ restricted to radial symmetric Bergman spaces to be a Hilbert-Schmidt operator. We also discuss compactness of the solution operator in spaces of entire functions in one variable. In the sequel we consider several examples and also treat the case of weighted spaces of entire functions...

We characterize the symbols φ for which there exists a weight w such that weighted composition operator MwCφ is compact on Bergman space Bα2. also bounded but not compact. investigate when Hilbert-Schmidt

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-d...

The Brockett-Wegner diagonalizing flow Ḣt = [ Ht, [Ht, A] ] is studied. Global existence and uniqueness of solutions of this evolution equation is proved on the space B[H ] of bounded operators on a complex Hilbert space H . Local existence is proved for certain unbounded initial operators H0. Furthermore, if H0, A are Hilbert-Schmidt operators, it is demonstrated that Ht strongly converges to ...

Inverse formulas for the tensor product are used to develop an algorithm to compute Schmidt decompositions of Finite Schmidt Rank (FSR) bounded operators on the tensor product of separable Hilbert spaces. The algorithm is then applied to solve inverse problems related to the tensor product of bounded operators. In particular, we show how properties of a FSR bounded operator are reflected by the...

Abstract: The classical Weyl-von Neumann theorem states that for any selfadjoint operator A in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C = C∗ such that the perturbed operator A + C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely define...

Composition operators Cφ on the Hilbert Hardy space H 2 over the unit disk are considered. We investigate when convergence of sequences {φn} of symbols, (i.e., of analytic selfmaps of the unit disk) towards a given symbol φ, implies the convergence of the induced composition operators, Cφn → Cφ . If the composition operators Cφn are Hilbert–Schmidt operators, we prove that convergence in the Hi...

We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. Fir...