Theses and Dissertations - UTB/UTPA

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Jasang Yoon

Second Advisor

Dr. Ramendra Krishna Bose

Third Advisor

Dr. Santanu Chakraborty


In mathematics, weighted shifts, also known as shift operators or translation operators, are examples of linear operators. Single and multivariable weighted shifts have played an important role in the study of (joint) k-hyponormality to LPCS. They have also played a significant role in the study of cyclicity and reflexivity, in the study of C*-algebras generated by multiplication operators on Bergman spaces, as fertile ground to test new hypotheses, and as canonical models for theories of dilation and positivity. We will first consider the hyponormality of powers of commuting multivariable weighted shifts. Specifically, if we let W(α,β) := (T1, T2) denote a commuting 2-variable weighted shift, we will prove that: (i) W(α,β) is hyponormal but [special characters omitted] is not hyponormal; and (ii) W(α,β) is not hyponormal but [special characters omitted] is hyponormal. In this work, we have expanded the results just mentioned above using the Smul'jan's test for the positivity of 2 × 2 block operators and the new direct sum decomposition for powers of 2-variable weighted shifts. As a consequence, we show that the 2-hyponormality of 2-variable weighted shifts are not invariant under powers.


Copyright 2011 Mayra O. Martinez. All Rights Reserved.

Granting Institution

University of Texas-Pan American