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THE STABILITY OF PROPERTY (gw) UNDER COMPACT PERTURBATION

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Abstract

Let \(\mathcal {H}\) be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on \(\mathcal {H}\) to satisfy that f(T) obeys property (g w) for each function f analytic on some neighborhood of σ(T). Also, we investigate the stability of property (g w) under (small) compact perturbations.

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Acknowledgments

The authors are grateful to the referee for several helpful suggestions concerning this paper

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mu’tah University, P.O.Box(7), Al-Karak, Jordan

    M. H. M. Rashid

  2. Department of Science and Humanities, Ahalia School of Engineering and Technology, Palakkad, 678557, Kerala, India

    T. Prasad

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  1. M. H. M. Rashid
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  2. T. Prasad
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Correspondence to M. H. M. Rashid.

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Rashid, M.H.M., Prasad, T. THE STABILITY OF PROPERTY (gw) UNDER COMPACT PERTURBATION. Acta Math Vietnam 39, 325–336 (2014). https://doi.org/10.1007/s40306-014-0065-0

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  • DOI: https://doi.org/10.1007/s40306-014-0065-0

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