Papers by Mohammadreza Azimi
Bulletin of the Korean Mathematical Society, 2010
In this note, we discuss measure theoretic characterizations for weighted composition operators i... more In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on L 2 (F) such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.
In this note we investigate the boundedness and boundedness from below of composition operators o... more In this note we investigate the boundedness and boundedness from below of composition operators on the weighted locally convex (WLC) space of measurable functions by Radon-Nikodym derivation and conditional expectation. Moreover, a subspace of these spaces is constructed in such a way that composition operators leave it invariant.
The Bulletin of the Malaysian Mathematical Society Series 2
In this paper we provide a necessary and sufficient condition for the conditional multiplication ... more In this paper we provide a necessary and sufficient condition for the conditional multiplication operators to have closed range. Also, some other properties of these type of operators will be investigated.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2011
We construct a Banach space operator T ∈ B(X) such that the set J T (0) has a nonempty interior b... more We construct a Banach space operator T ∈ B(X) such that the set J T (0) has a nonempty interior but J T (0) = X. This gives a negative answer to a problem raised by G. Costakis and A. Manoussos. 1991 Mathematics Subject Classification. 47A16.
A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators between separable Banach spaces $... more A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators between separable Banach spaces $X, Y$ is called diskcyclic if there exists a vector $x\in X$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1\}$ is dense in $Y$. In the first section of this paper we study some conditions that imply the diskcyclicity of $\{T_n\}_{n=1}^{\infty}$. In particular, a sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators on separable infinite dimensional Hilbert space $\mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $M\subseteq \mathcal{H},$ if there exists a vector $x\in \mathcal{H}$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1\}\cap M$ is dense in $M$. In the second section we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by the some mathematicians in \cite{MR2261697, MR2720700, MR1111569}) ...
In this paper we first introduce the extended limit set $J_{\{T^n\}}(x)$ for a sequence of bounde... more In this paper we first introduce the extended limit set $J_{\{T^n\}}(x)$ for a sequence of bounded linear operators $\{T_n\}_{n=1}^{\infty}$ on a separable Banach space $X$ . Then we study the dynamics of sequence of linear operators by using the extended limit set. It is shown that the extended limit set is strongly related to the topologically transitive of a sequence of linear operators. Finally we show that a sequence of operators $\{T_n\}_{n=1}^{\infty}\subseteq \mathcal{B}(X)$ is hypercyclic if and only if there exists a cyclic vector $x\in X$ such that $J_{\{T^n\}}(x)=X$.
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Papers by Mohammadreza Azimi