2015
DOI: 10.1360/012015-8
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Generalized Weyl's theorem and spectral continuity for (<italic>n</italic>, <italic>k</italic>)-quasiparanormal operators

Abstract: If T or T * is a totally (n, k)-quasiparanormal operator acting on an infinite dimensional separable Hilbert space, then we prove that generalized Weyl's theorem holds for f (T) for every f ∈ H(σ(T)) which is nonconstant on each connected component of its domain. Moreover, if T * is a totally (n, k)-quasiparanormal operator, then generalized a-Weyl's theorem holds for f (T) for every f ∈ H(σ(T)) which is nonconstant on each connected component of its domain. Also, we prove that the spectrum is continuous on th… Show more

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“…Recently Yuan and Gao [5] introduced class ( ) (i.e., | 1+ | 2/(1+ ) ≥ | | 2 ) operators and -paranormal operators (i.e., ‖ 1+ ‖ 1/(1+ ) ≥ ‖ ‖ for every unit vector ∈ H) for some positive integer . For more interesting properties on class ( ) andparanormal operators, see [5][6][7][8].…”
Section: Introductionmentioning
confidence: 99%
“…Recently Yuan and Gao [5] introduced class ( ) (i.e., | 1+ | 2/(1+ ) ≥ | | 2 ) operators and -paranormal operators (i.e., ‖ 1+ ‖ 1/(1+ ) ≥ ‖ ‖ for every unit vector ∈ H) for some positive integer . For more interesting properties on class ( ) andparanormal operators, see [5][6][7][8].…”
Section: Introductionmentioning
confidence: 99%