Common Supercyclic Vectors for a Path of Operators

Authors

Kit C. Chan, Bowling Green State UniversityFollow
Rebecca Sanders, Marquette UniversityFollow

Document Type

Article

Language

eng

Publication Date

1-1-2008

Publisher

Elsevier

Source Publication

Journal of Mathematical Analysis and Applications

Source ISSN

0022-247X

Abstract

We examine common supercyclic vectors for a path of operators. In particular, we show that the path consisting of convex combinations of two arbitrary unilateral weighted backward shifts has a dense G_δ set of common supercyclic vectors. Moreover, we show there exists a path with a dense G_δ set of common supercyclic vectors between a unilateral weighted backward shift which satisfies the Supercyclicity Criterion, and an operator which does not. Lastly, we provide an example of a path of unilateral weighted backward shifts that fails to have a common supercyclic vector.

Comments

Journal of Mathematical Analysis and Applications, Vol. 337, No. 1 (January 1, 2008): 646-658. DOI.

Recommended Citation

Chan, Kit C. and Sanders, Rebecca, "Common Supercyclic Vectors for a Path of Operators" (2008). Mathematics, Statistics and Computer Science Faculty Research and Publications. 599.
https://epublications.marquette.edu/mscs_fac/599