Cyclicity of Vectors with Orbital Limit Points for Backward Shifts

Author(s)

Kit C. Chan, Bowling Green State UniversityFollow
Irina Seceleanu

Document Type

Article

Abstract

On a separable, infinite dimensional Banach space X, a bounded linear operator T : X → X is said to be hypercyclic, if there exists a vector x in X such that its orbit Orb(T, x) = {x, Tx, T2x, …} is dense in X. In a recent paper (Chan and Seceleanu in J Oper Theory 67:257–277, 2012), it was shown that if a unilateral weighted backward shift has an orbit with a single non-zero limit point, then it possesses a dense orbit, and hence the shift is hypercyclic. However, the orbit with the non-zero limit point may not be dense, and so the vector x inducing the orbit need not be hypercyclic. Motivated by this result, we provide conditions for x to be a cyclic vector.

Repository Citation

Chan, Kit C. and Seceleanu, Irina, "Cyclicity of Vectors with Orbital Limit Points for Backward Shifts" (2014). Mathematics and Statistics Faculty Publications. 32.
https://scholarworks.bgsu.edu/math_stat_pub/32

Publication Date

2014

Publication Title

Integral Equations and Operator Theory

DOI

https://doi.org/10.1007/s00020-013-2100-2

Volume

78

Start Page No.

225

End Page No.

232