2021/12/16 by Baranov, Anton, Lishanskii, Andrei
#30H10 #47A16 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2112.08813
In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and antianalytic parts. We show that, for a class of model spaces, truncated Toeplitz operators with symbols of the form Φ(z) =a z +b + cz, |a| ≠ |c|, have complete sets of eigenvectors, and, in particular, are not hypercyclic.