It is proved that in Hilbert spaces a single Hilbert–Schmidt operator radonifies cylindrical semimartingales to strong semimartingales. This improves a result due to Badrikian and¨Ustünel (also L. Schwartz), who needed composition of three Hilbert–Schmidt operators.

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases. Then we construct Bessel sequences frames and Riesz bases for the class of Hilbert Schmidt operators using the tensor product of such sequences in the original...

Abstract. We first show that the canonical solution operator to ∂ restricted to (0, 1)forms with holomorphic coefficients can be expressed by an integral operator using the Bergman kernel. This result is used to prove that in the case of the unit disc in C the canonical solution operator to ∂ restricted to (0, 1)-forms with holomorphic coefficients is a Hilbert-Schmidt operator. In the sequel w...

let ? be an open connected subset of the complex plane c and let t be a bounded linear operator on a hilbert space h. for ? in ? let e the orthogonal projection onto the null-space of t-?i . we discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. a generalized gram- schmidt process is also given.

We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence classes of bipartite states. Each class consists of all the density operators (in a given bipartite Hilbert space) sharing the same set of Schmidt coefficients. N...

We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the basic separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly,...

Randomly correlated ensembles of two quantum systems are investigated, including average entanglement entropies and probability distributions of Schmidt-decomposition coefficients. Maximal correlation is guaranteed in the limit as one system becomes infinite-dimensional. The reduced density operator distributions are compared with distributions induced via the Bures and Hilbert-Schmidt metrics....

We give dimension-free and data-dependent bounds for linear multi-task learning where a common linear operator is chosen to preprocess data for a vector of task specific linear-thresholding classifiers. The complexity penalty of multi-task learning is bounded by a simple expression involving the margins of the task-specific classifiers, the Hilbert-Schmidt norm of the selected preprocessor and ...