On linear chaos in function spaces

Abstract

We show that, in Lp(0,∞){L}_{p}\left(0,\infty ) (1≤p<∞1\le p\lt \infty ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞){C}_{0}{[}0,\infty ) and describe the spectra of the weighted translations provided the underlying spaces are complex.

Keywords

• hypercyclic vector
• periodic point
• hypercyclic operator
• chaotic operator
• spectrum
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