#### Date of Award

Spring 1993

#### Project Type

Dissertation

#### Program or Major

Mathematics

#### Degree Name

Doctor of Philosophy

#### First Advisor

Eric Nordgren

#### Abstract

In this paper we consider the Hankel operators from two points of view. On one hand the Hankel operator is induced by the coefficient sequence $a\sb0,a\sb1,a\sb2,\...$ and operates on a Hilbert space $H\sp2(\beta)$ with $\Sigma\sbsp{n=0}{\infty}\ \beta(n)\sp2 < \infty.$ In this situation we can find necessary conditions and sufficient conditions for the Hankel operator to be bounded. However, with compactness and Hilbert-Schmidt we can get only sufficient conditions. On the other hand we look at the Hankel operator $H\sb{f,\alpha}$ and little Hankel operator $h\sb{f,\alpha},$ with symbol function f, that operates on a weighted Bergman space. In this case we can determine bounded, compact, Hilbert Schmidt, or trace class operators of the Hankel operator $H\sb{f}$ and $h\sb{f,\alpha}.$ We also give a good estimate of bounded norm of little Hankel operators with a particular symbol function $f = z\bar g$ where g is in the Bloch space.

#### Recommended Citation

Wanpen, Pachara, "Hankel operators on Hilbert spaces" (1993). *Doctoral Dissertations*. 1744.

https://scholars.unh.edu/dissertation/1744