Date of Award

5-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

William R. Parzynski

Committee Member

Ted Williamson

Committee Member

Diana M. Thomas

Abstract

In this paper, we examine the weighted shift operator in l2 as described in Yoo & Rho [15], which is an example of what is known as a hyponormal weighted shift. Using the methods of Tam [13], in conjuction with properties of the weighted shift, we determine the numerical range of Yoo &; Rho’s unilateral weighted shift operator.

It is well-established that the spectrum of a bounded linear operator is always included in the closure of the numerical range. In particular, for a bounded linear operator, the point and compression spectra are contained within the numerical range itself [7]. We wish to take this, as well as other information we know pertaining to the numerical range, and determine the location of the residual, continuous, and approximate point spectra of Yoo &; Rho’s unilateral weighted shift operator within the closure of the numerical range.

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