Aluthge operator field and its numerical range and spectral properties - Archive ouverte HAL
Article Dans Une Revue Integral Equations and Operator Theory Année : 2021

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.
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Dates et versions

hal-02995331 , version 1 (09-11-2020)

Identifiants

Citer

Gilles Cassier, Thomas Perrin. Aluthge operator field and its numerical range and spectral properties. Integral Equations and Operator Theory, 2021, 93 (4), Article 41 (20 p.). ⟨10.1007/s00020-021-02656-2⟩. ⟨hal-02995331⟩
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