Quadratically hyponormal recursively generated weighted shifts need not be positively quadratically hyponormal

Authors

• Yiu T. Poon, Iowa State University
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

8-1-2007

Abstract

We study a class of weighted shifts W α defined by a recursively generated sequence α ≡ α0, ... , α m-2, (α m-1, α m , α m+1)^∧ and characterize the difference between quadratic hyponormality and positive quadratic hyponormality. We show that a shift in this class is positively quadratically hyponormal if and only if it is quadratically hyponormal and satisfies a finite number of conditions. Using this characterization, we give a new proof of [12, Theorem 4.6], that is, for m = 2, W α is quadratically hyponormal if and only if it is positively quadratically hyponormal. Also, we give some new conditions for quadratic hyponormality of recursively generated weighted shift W α (m ≥ 2). Finally, we give an example to show that for m ≥ 3, a quadratically hyponormal recursively generated weighted shift W α need not be positively quadratically hyponormal.

Comments

© 2007 Birkhäuser Verlag Basel/Switzerland.

Recommended Citation

Poon, Yiu T., and Jasang Yoon. "Quadratically hyponormal recursively generated weighted shifts need not be positively quadratically hyponormal." Integral Equations and Operator Theory 58, no. 4 (2007): 551-562. https://doi.org/10.1007/s00020-007-1505-1

First Page

551

Last Page

562

Publication Title

Integral Equations and Operator Theory

DOI

10.1007/s00020-007-1505-1