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Weyl’s theorem for algebraically wF(p, r, q) operators with p, r > 0 and q ≥ 1

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Ukrainian Mathematical Journal Aims and scope

If T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting in an infinite-dimensional separable Hilbert space, then we prove that Weyl’s theorem holds for f(T) for any f ∈ Hol(σ(T)), where Hol(σ(T)) is the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl’s theorem holds for f(T). In addition, if T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1, then we establish the spectral mapping theorems for the Weyl spectrum and for the essential approximate point spectrum of T for any f ∈ Hol(σ(T)), respectively. Finally, we examine the stability of Weyl’s theorem and the a-Weyl’s theorem under commutative perturbations by finite-rank operators.

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Authors and Affiliations

  1. Mu’tah University, Al-Karak, Jordan

    M. H. M. Rashid

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  1. M. H. M. Rashid
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 8, pp. 1092–1102, August, 2011.

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Rashid, M.H.M. Weyl’s theorem for algebraically wF(p, r, q) operators with p, r > 0 and q ≥ 1. Ukr Math J 63, 1256–1267 (2012). https://doi.org/10.1007/s11253-012-0576-6

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  • DOI: https://doi.org/10.1007/s11253-012-0576-6

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