Hypercyclicity of adjoint of convex weighted shift and multiplication operators on Hilbert spaces

Document Type : Original Article


Department of Basic Science, Hamedan University of Technology, Hamedan, Iran.


A bounded linear operator $T$ on a Hilbert space $\mathfrak{H}$ is
convex, if
$$\|\mathfrak{T}^{2}v\|^2-2\|\mathfrak{T}v\|^2+\|v\|^2 \geq 0.$$
In this paper, sufficient conditions to hypercyclicity of adjoint of unilateral (bilateral) forward (backward) weighted shift operator is given. Also, we present some example of convex operators such that it's adjoint is hypercyclic. Finally, the spectrum of convex multiplication operators is obtained and an example of convex, multiplication operators is given such that it's adjoint is hypercyclic.