关于拟相似于等距算子的等距渐近线
On isometric asymptotes of operators quasisimilar to isometries
AI总结：
本文构造了拟相似于等距算子但没有等距渐近线的算子，以及一个拟相似于无限重数单侧移位且等距渐近线含非零酉直和项的收缩算子。
摘要：
等距和酉渐近线的概念于1989年为幂有界算子引入，并在2016至2019年间由Kérchy推广。特别地，研究表明存在没有酉渐近线的算子。本文构造了拟相似于等距算子且没有等距渐近线的算子。此外，还构造了一个收缩算子，它拟相似于无限重数的单侧移位，且其等距渐近线包含一个（非零）酉直和项。
英文摘要：
The notion of isometric and unitary asymptotes was introduced for power bounded operators in 1989 and was generalized in 2016--2019 by Kérchy. In particular, it was shown that there exist operators without unitary asymptote. In this paper operators are constructed which are quasisimilar to isometries and do not have isometric asymptotes. Also a contraction is constructed which is quasisimilar to the unilateral shift of infinite multiplicity and whose isometric asymptote contains a (non-zero) unitary summand.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
