Toral and spherical Aluthge transforms of 2-variable weighted shifts

Raúl E. Curto; Jasang Yoon

doi:10.1016/j.crma.2016.10.005

Functional analysis

Toral and spherical Aluthge transforms of 2-variable weighted shifts
[Transformations d'Aluthge torales et sphériques de shifts pondérés à deux variables]

Présenté par : Gilles Pisier

Raúl E. Curto ¹ ; Jasang Yoon ²

¹ Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
² School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1200-1204.

Résumé
Abstract

Nous introduisons deux notions naturelles des transformations d'Aluthge (torales et sphériques) pour les shifts pondérés à deux variables et nous étudions leurs propriétés. Ensuite, nous étudions la classe de shifts pondérés à deux variables sphériques et quasi-normaux, qui sont les points fixes pour la transformation d'Aluthge sphérique. Enfin, nous discutons brièvement la relation entre les shifts pondérés à deux variables qui sont sphériquement quasinormaux et ceux qui sont sphériquement isométriques.

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.

Reçu le : 2016-06-07
Accepté le : 2016-10-07
Publié le : 2016-10-18

DOI : 10.1016/j.crma.2016.10.005

Affiliations des auteurs :

Raúl E. Curto ¹ ; Jasang Yoon ²

¹ Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
² School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA

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     title = {Toral and spherical {Aluthge} transforms of 2-variable weighted shifts},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1200--1204},
     publisher = {Elsevier},
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     number = {12},
     year = {2016},
     doi = {10.1016/j.crma.2016.10.005},
     language = {en},
}

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Raúl E. Curto; Jasang Yoon. Toral and spherical Aluthge transforms of 2-variable weighted shifts. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1200-1204. doi : 10.1016/j.crma.2016.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.10.005/

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Cité par Sources :

^☆ The first author of this paper was partially supported by NSF Grant DMS-1302666.

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