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...

The paper is devoted to an invertible linear operator whose inverse is a Hilbert Schmidt operator and imaginary Hermitian component is bounded. Numerous regular differential and integro-differential operators satisfy these conditions. A sharp norm estimate for the resolvent of the considered operator is established. It gives us estimates for the semigroup and so-called Hirsch operator functions...

Trace class operators Cont Last time I define and operator to be of 'trace class' if it is a finite sum of products of Hilbert-Schmidt operators (1) T =

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

In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and sh...

In this paper we show that the output of a nonlinear system with inputs in (L2 [0, T]; R ' ) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via t...