论文标题
关于布鲁内尔运营商界限的新估计
New Estimates on the bounds of Brunel's operator
论文作者
论文摘要
我们研究了功能$ψ（x）= \ frac {1- \ sqrt {1-x}} {x} $的泰勒系列功能的系数扩展，其中brunel operator $ a \ equiv a \ equiv a（t）$被定义为$ t $ t $ t $ t $ t $ t $ t $ t $ t $。我们证明了有关$ n \ in \ mathbb {n} $的$ψ^n $的泰勒系数的几个新的精确估计。我们应用这些估计值提供了一个基本证明，即对于任何卑鄙的（不一定是正面运算符）$ x $上的均值$ t $，brunel运算符$ a（t）：x \ to x $是有能力的，可以满足$ \ sup_ {n \ in \ sup_ {n \ in \ mathbbb {n}}}}}} \ | n（a^n-i^n> a^n> a^a^n>}） <\ infty $（等效地，$ a（t）$是RITT操作员）。在途中，我们提供了A. Brunel和R. Emilion在\ cite {Brunel}中宣布的结果的具体细节。
We study the coefficients of the Taylor series expansion of powers of the function $ψ(x)=\frac{1-\sqrt{1-x}}{x}$, where the Brunel operator $A\equiv A(T)$ is defined as $ψ(T)$ for any mean-bounded $T$. We prove several new precise estimates regarding the Taylor coefficients of $ψ^n$ for $n\in\mathbb{N}$. We apply these estimates to give an elementary proof that for any mean-bounded, not necessarily positive operator $T$ on a Banach space $X$, the Brunel operator $A(T):X\to X$ is power-bounded and satisfies $\sup_{n\in\mathbb{N}} \|n(A^n-A^{n+1})\| < \infty$ (equivalently, $A(T)$ is a Ritt operator). Along the way we provide specific details of results announced by A. Brunel and R. Emilion in \cite{Brunel}.
