This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients {〈k,Φm,n〉} of certain frame expansions of the kernel k of an integral operator are in l, then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a parti...

In this paper, we characterize holomorphic functions / such that the Hankel operators Hj are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for p > In , Hj is in the Schatten class Sp if and only if / is in the Besov space Bp ; for p < In , Hj is in the Schatten class Sp if and only if / = constant.

in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators  are investigated.

The first main result in this article provides an error bound for balanced truncation where the matrix norm used is a general Schatten norm rather than the usual operator norm. The second main result in this article is that for the Schatten 1-norm (the trace class norm) this bound, for systems with a semi-definite Hankel operator, is in fact an equality. This class of systems for which we obtai...

Let A be a C∗-algebra. We prove that every absolutely summing operator from A into l2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite dimensional examples that show that one can not replace the 4-Schatten-von Neumann class by p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of cap...

We apply the complex interpolation method to prove that, given two spacesB p0,a;s0 , B (n) p1,b;s1 of n-tuples of operators in the p-Schatten class of a Hilbert space H , endowed with weighted norms associated to positive and invertible operators a and b of B(H) then, the curve of interpolation (B p0,a;s0 , B (n) p1,b;s1 )[t] of the pair is given by the space of n-tuples of operators in the pt-...