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Acta Mathematica Vietnamica

, Volume 42, Issue 4, pp 747–759 | Cite as

Property (a B w) and Weyl Type Theorems

  • Mohammad H. M. RashidEmail author
Article
  • 66 Downloads

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 TS obeys property (a B w).

Keywords

Generalized Weyl’s theorem Generalized a-Weyl’s theorem Polaroid operators SVEP Property (aBw

Mathematics Subject Classification (2010)

47A53 47A55 47A10 47A11 47A20 

Notes

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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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of ScienceMu’tah UniversityAl-karakJordan

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