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ALUTHGE OPERATOR FIELD AND ITS NUMERICAL RANGE AND SPECTRAL PROPERTIES

Abstract : For an arbitrary operator T acting on a Hilbert space we consider a field of operators (∆ z (T)) called the Aluthge operator field associated with T . 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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https://hal.archives-ouvertes.fr/hal-02995331
Contributor : Gilles Cassier <>
Submitted on : Monday, November 9, 2020 - 10:08:06 AM
Last modification on : Monday, November 16, 2020 - 9:12:25 AM

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  • HAL Id : hal-02995331, version 1

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Gilles Cassier, Thomas Perrin. ALUTHGE OPERATOR FIELD AND ITS NUMERICAL RANGE AND SPECTRAL PROPERTIES. 2020. ⟨hal-02995331⟩

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