Positive Hankel Operators of Schatten p-classes

Abstract

In this thesis, we consider positive Hankel operators of Schatten p-classes. It was known that for every positive semidefinite Hankel operator $\mathnormal{H}_{\mu} =(\mu_{j+k})_{j,k\ge0}$, $\mathnormal{H}_{\mu}$ is bounded if and only if $

\mu_{n}

(1+n)$ is bounded, and that $\mathnormal{H}_{\mu}$ is compact if and only if $

(1+n)\to 0$. The main result of this thesis is that a general bounded positive semidefinite $\mathnormal{H}_{\mu}$ is of Schatten p-class if and only if $\sum_{n=0}^{\infty}(n+1)^{p-1}

^p<\infty$.