Aluthge operator field and its numerical range and spectral properties
Résumé
For an arbitrary operator T acting on a Hilbert space we consider a field of operators (∆ z (T)) called the Aluthge operator field associated withT . After giving preliminary results, we establish that two fields (left and right), canonically linked to the Altuthge field (∆ z (T)) and a support subspace, are constant on each horizontal segment where they are defined. This result leads to a positive solution of a conjecture stated by Jung-Ko-Pearcy in 2000. Then we do a detailed spectral study of (∆ z (T)) and we give a Yamazaki type formula in this context.
Domaines
Analyse fonctionnelle [math.FA]Origine | Fichiers produits par l'(les) auteur(s) |
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