Spectral pictures of 2-variable weighted shifts

Authors

• Raúl E. Curto, University of Iowa
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

11-1-2006

Abstract

We study the spectral pictures of (jointly) hyponormal 2-variable weighted shifts with commuting subnormal components. By contrast with all known results in the theory of subnormal single and 2-variable weighted shifts, we show that the Taylor essential spectrum can be disconnected. We do this by obtaining a simple sufficient condition that guarantees disconnectedness, based on the norms of the horizontal slices of the shift. We also show that for every k ≥ 1 there exists a k-hyponormal 2-variable weighted shift whose horizontal and vertical slices have 1- or 2-atomic Berger measures, and whose Taylor essential spectrum is disconnected.

Comments

© 2006 Académie des sciences.

http://www.elsevier.com/open-access/userlicense/1.0/

Recommended Citation

Curto, Raúl E., and Jasang Yoon. "Spectral pictures of 2-variable weighted shifts." Comptes rendus. Mathématique 343, no. 9 (2006): 579-584. https://doi.org/10.1016/j.crma.2006.09.024

First Page

579

Last Page

584

Publication Title

Comptes Rendus Mathematique

DOI

10.1016/j.crma.2006.09.024