Journal of Operator Theory

Volume 59, Issue 1, Winter 2008 pp. 193-210.

Spectral pictures of operator-valued weighted bi-shifts

Authors: Abdellatif Bourhim
Author institution: Departement de mathematiques et de statistique, Universite Laval, Quebec (Quebec), Canada G1K 7P4

Summary: In this paper, we introduce operator-valued weighted bi-shifts on the Hilbert space

$l^2(\N,\h)$ , of all square-summable sequences whose elements are in a complex Hilbert space

$\h$ , and study their spectral and local spectral properties. We determine the spectrum and its parts of such bi-shifts, and compute their local spectrum at most points of

$l^2(\N,\h)$ . Furthermore, we provide necessary and sufficient conditions for an operator-valued weighted bi-shift to enjoy the single-valued extension property.

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