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Semi-generalized Partial Isometries

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Abstract

The purpose of this paper is to present in Hilbert spaces some results for a new class of operators called semi-generalized partial isometries which include two important classes in operator theory: partial isometries and nilpotent operators. We prove some basic properties and decomposition theorems. Some spectral theorems for this class of operators are also given. Part of the results proved in this paper improve and generalize some results known for partial isometries.

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Acknowledgements

We want to thank the referee for reading this paper carefully, whose generous and valuable remarks and comments brought improvements to the paper and enhance clarity.

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Authors and Affiliations

  1. Département de Mathématiques, Institut Supérieur des Sciences Appliquées et de Technologie de Kairouan, Avenue Beit El Hikma, 3100, Kairouan, Tunisia

    Zied Garbouj

  2. Département de Mathématiques, Faculté des Sciences de Monastir, Avenue de l’environnement, 5019, Monastir, Tunisia

    Haïkel Skhiri

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  1. Zied Garbouj
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  2. Haïkel Skhiri
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Correspondence to Haïkel Skhiri.

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The work of Zied Garbouj and Haïkel Skhiri was supported by LR/18/ES/16: Analyse, Géométrie et Applications, University of Monastir (Tunisia).

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Garbouj, Z., Skhiri, H. Semi-generalized Partial Isometries. Results Math 75, 15 (2020). https://doi.org/10.1007/s00025-019-1143-3

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