Triangular extension spectrum

of weighted shifts

Author:
Zhidong Pan

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3293-3298

MSC (1991):
Primary 47A15, 47A45, 47C05

MathSciNet review:
1476383

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Abstract | References | Similar Articles | Additional Information

Abstract: A necessary and sufficient condition for a complex number to be in the triangular extension spectrum of a weighted backward shift is obtained. It is shown that the triangular extension spectrum of a weighted backward shift is always a closed annulus when it is not empty. Moreover, for any given closed annulus, there exists a weighted backward shift with the annulus as its triangular extension spectrum.

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Additional Information

**Zhidong Pan**

Affiliation:
Department of Mathematics, Saginaw Valley State University, University Center, Michigan 48710

Email:
pan@tardis.svsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04692-9

Keywords:
Operator,
triangular,
semitriangular,
extension,
spectrum

Additional Notes:
This work was supported in part by a research release time award from Saginaw Valley State University

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society