Qom University of TechnologyMathematics and Computational Sciences2717-27082420211201Hypercyclicity of adjoint of convex weighted shift and multiplication operators on Hilbert spaces525924723510.30511/mcs.2021.539285.1039ENLotfollahKarimiDepartment of Basic Science, Hamedan University of Technology, Hamedan, Iran.Journal Article20210919A bounded linear operator $T$ on a Hilbert space $\mathfrak{H}$ is convex, if <br />$$\|\mathfrak{T}^{2}v\|^2-2\|\mathfrak{T}v\|^2+\|v\|^2 \geq 0.$$ <br />In this paper, sufficient conditions to hypercyclicity of adjoint of unilateral (bilateral) forward (backward) weighted shift operator is given. Also, we present some examples 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.http://mcs.qut.ac.ir/article_247235_f3a2809ba19f34d48dbc5b1421532f4f.pdf