Date of Award
Master of Science (MS)
College of Science and Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
William R. Parzynski
Diana M. Thomas
In this paper, we examine the weighted shift operator in l2 as described in Yoo & Rho , which is an example of what is known as a hyponormal weighted shift. Using the methods of Tam , 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 . 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.
Santamaria, Gina-Louise, "On the Numerical Range and Spectrum of the Weighted Shift Operator in [iota]²" (2010). Theses, Dissertations and Culminating Projects. 972.