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عنوان
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subspace-hypercyclic conditional weighted composition operators on $L^p$-spaces
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نوع پژوهش
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مقاله چاپشده در مجلات علمی
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کلیدواژهها
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Subspace-hypercyclic, Orbit, Subspace-weakly mixing, Subspace-topologically mixing, Measurable transformation, Normal, Radon-Nikodym derivative, Conditional expectation, aperiodic.
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چکیده
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A conditional weighted composition operator $T_u: L^p(\Sigma)\rightarrow L^p(\mathcal{A})$ ($1\leq p<\infty$), is defined by $T_u(f):= E^{\mathcal{A}}(u f\circ \varphi)$, where $\varphi: X\rightarrow X$ is a measurable transformation, $u$ is a weight function on $X$ and $E^{\mathcal{A}}$ is the conditional expectation operator with respect to $\mathcal{A}$. In this paper, we study the subspace-hypercyclicity of $T_u$ with respect to $L^p(\mathcal{A})$. First, we show that if $\varphi$ is a periodic nonsingular transformation, then $T_u$ is not $L^p(\mathcal{A})$-hypercyclic. The necessary conditions for the subspace-hypercyclicity of $T_u$ are obtained when $\varphi$ is non-singular and finitely non-mixing. For the sufficient conditions, the normality of $\varphi$ is required. The subspace-weakly mixing and subspace-topologically mixing concepts are also studied for $T_u$. Finally, we give an example which is subspace-hypercyclic while is not hypercyclic.
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پژوهشگران
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محمدرضا عظیمی (نفر اول)، زینب نقدی (نفر دوم)
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