Geodesic
Judgement of two Weyl type theorems for bounded linear operators
Filomat, Tome 37 (2023) no. 23, p. 7771

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DOI

Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. T ∈ B(H) is said to satisfy property (UW Π) if σ a (T)\σ ea (T) = Π(T), where σ a (T) and σ ea (T) denote the approximate point spectrum and the essential approximate point spectrum of T respectively, Π(T) denotes the set of all poles of T. T ∈ B(H) satisfies a-Weyl's theorem if σ a (T)\σ ea (T) = π a 00 (T), where π a 00 (T) = {λ ∈ isoσ a (T): 0 n(T − λI) ∞}. In this paper, we give necessary and sufficient conditions for a bounded linear operator and its function calculus to satisfy both property (UW Π) and a-Weyl's theorem by topological uniform descent. In addition, the property (UW Π) and a-Weyl's theorem under perturbations are also discussed.
DOI : 10.2298/FIL2323771Z
Classification : 47A10, 47A53, 47A55
Keywords: property (UWΠ), a-Weyl’s theorem, topological uniform descent, perturbation 
Tengjie Zhang; Xiaohong Cao. Judgement of two Weyl type theorems for bounded linear operators. Filomat, Tome 37 (2023) no. 23, p. 7771 . doi: 10.2298/FIL2323771Z
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     title = {Judgement of two {Weyl} type theorems for bounded linear operators},
     journal = {Filomat},
     pages = {7771 },
     year = {2023},
     volume = {37},
     number = {23},
     doi = {10.2298/FIL2323771Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2323771Z/}
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