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Property (a B w) and Weyl Type Theorems

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Abstract

In this paper, we introduces the property (a B w), a variant of generalized a-Weyl’s theorem for a bounded linear operator T on an infinite-dimensional Banach space \(\mathbb {X}\). We establish several sufficient and necessary conditions for which property (a B w) holds. Also, we prove that if \(T\in \mathbf {L(\mathbb {X})}\) satisfies property (a B w) then T satisfies property (B w). Certain conditions are explored on Hilbert space operators T and S so that T ⊕ S obeys property (a B w).

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Acknowledgements

The author would like to express their sincere appreciation to the referees for their very helpful suggestions and many kind comments.

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Authors and Affiliations

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

    Mohammad H. M. Rashid

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  1. Mohammad H. M. Rashid
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Correspondence to Mohammad H. M. Rashid.

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Rashid, M. Property (a B w) and Weyl Type Theorems. Acta Math Vietnam 42, 747–759 (2017). https://doi.org/10.1007/s40306-017-0222-3

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  • DOI: https://doi.org/10.1007/s40306-017-0222-3

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