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A bounded linear operator T on a Hilbert space H is convex, if for each x ∊ H, ‖T²x‖² -- 2‖Tx‖² + ‖x‖² ≥ 0. In this paper, it is shown that if T is convex and supercyclic then it is a contraction or an expansion. We then present some examples of convex supercyclic operators. Also, it is proved that no convex composition operator induced by an automorphism of the disc on a weighted Hardy space is supercyclic. [ABSTRACT FROM AUTHOR]

A bounded linear operator T on a Hilbert space is an isometric N-Jordan operator if it can be written as A + Q, where A is an isometry and Q is a nilpotent of order N such that AQ = QA. In this paper, we will show that the only isometric N-Jordan weighted shift operators are isometries. This answers a question recently raised. [ABSTRACT FROM AUTHOR]

We characterize the commutants of some multiplication operators on a Banach space of analytic functions defined on a bounded domain in the plane. Under certain conditions on the symbol of a multiplication operator, we show that its commutant is a set of multiplication operators. This partially answers a question of Axler, Cuckovic and Rao. Next, the hyper-reflexivity of these multiplication operators are proved. The paper is concluded by proving the hyper-reflexivity of the multiplication operators with symbols φ(z)= z, k =1, 2,... . [ABSTRACT FROM AUTHOR]

Let Mz and B denote, respectively, the multiplication operator and the backward shift operator on a weighted Hardy space. We present sufficient conditions so that Mzn is similar to ..., and Bn is similar to ... The first part generalizes a result obtained by Yucheng Li. [ABSTRACT FROM AUTHOR]