Toral and spherical Aluthge transforms of 2-variable weighted shifts
نویسندگان
چکیده
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. To cite this article: R. Curto, J. Yoon, C. R. Acad. Sci. Paris, Ser. I (2016).
منابع مشابه
Aluthge transforms of 2-variable weighted shifts
We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, in sharp contrast with the 1-variable case. Second, we identify a large class of 2-variable weighted shifts for which hyponormality is pres...
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