论文标题
$ l^p $ - 空间上的子空间 - 杂交条件类型运算符
Subspace-hypercyclic conditional type operators on $L^p$-spaces
论文作者
论文摘要
有条件加权组成 操作员$ t_u：l^p（σ）\ rightarrow l^p（\ nathcal {a}）$（$ 1 \ leq p <\ infty $）由$ t_u（f）：= e^e^{\ nathcal {a}}}（u f \ f \ circou） $ x $和$ e^{\ mathcal {a}} $的功能是相对于$ \ Mathcal {a} $的有条件期望运算符。在本文中，我们研究了$ t_u $的子空间hyperclyclicity相对于$ l^p（\ Mathcal {a}）$。首先，我们表明，如果$φ$是一种周期性的非主流转换，则$ t_u $不是$ l^p（\ nathcal {a}）$ - hypercyclic。当$φ$是非单一的且有限的非混合时，可以获得$ t_u $的子空间hyperclyclicity的必要条件。对于足够的条件，需要$φ$的正态性。还研究了$ t_u $的子空间混合和子空间混合概念。最后，我们举一个示例，该示例是子空间杂种，而不是超环状。
A conditional weighted composition operator $T_u: L^p(Σ)\rightarrow L^p(\mathcal{A})$ ($1\leq p<\infty$), is defined by $T_u(f):= E^{\mathcal{A}}(u f\circ φ)$, where $φ: X\rightarrow X$ 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 $φ$ 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 $φ$ is non-singular and finitely non-mixing. For the sufficient conditions, the normality of $φ$ 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.
