标题： 环形和球形 Aluthge 变换的$2$变量加权位移 显示英文标题

标题： Toral and spherical Aluthge transforms of $2$-variable weighted shifts

摘要： 我们引入了二维加权移位的两个自然的Aluthge变换概念（环形和球形），并研究它们的基本性质。 接下来，我们研究球形准正则的$2$-变量加权移位类，这些是球形Aluthge变换的不动点。 最后，我们简要讨论球形准正则与球形等距二维加权移位之间的关系。 显示英文摘要

摘要： We introduce two natural notions of Aluthge transforms (toral and spherical) for 2-variable weighted shifts and study their basic properties. Next, we study the class of spherically quasinormal $2$-variable weighted shifts, which are the fixed points for the spherical Aluthge transform. Finally, we briefly discuss the relation between spherically quasinormal and spherically isometric 2-variable weighted shifts.