论文标题
渐近极限，BANACH极限和CESàRO意味着
Asymptotic limits, Banach limits, and Cesàro means
论文作者
论文摘要
希尔伯特空间中的每一个新产品都是通过独特的正算子$ $。$。本文的第一部分是对这种技术的应用的调查，包括与同音相似的表征$。$第二部分重点介绍了与电力界操作员交易的Banach限制。结果表明，如果一个偏移的cesàRo序列在移位参数中均匀收敛（至少在弱拓扑中），则它具有与所有Banach Limits $φ$相一致的cesàRo渐近极限。
Every new inner product in a Hilbert space is obtained from the original one by means of a unique positive operator$.$ The first part of the paper is a survey on applications of such a technique, including a characterization of similarity to isometries$.$ The second part focuses on Banach limits for dealing with power bounded operators. It is shown that if a power bounded operator for which the sequence of shifted Cesàro means converges (at least in the weak topology) uniformly in the shift parameter, then it has a Cesàro asymptotic limit coinciding with its $φ$-asymptotic limit for all Banach limits $φ$.
