Research Article

New approach to property (ω) for functions of operators

Published in: Quaestiones Mathematicae
Volume 46 , issue 2 , 2023 , pages: 335–346

DOI: 10.2989/16073606.2021.2014593

Author(s): Xiaohong Cao School of Mathematics and Statistics, Shaanxi Normal University, People’s Republic of China , Lili Yang School of Mathematics and Statistics, Shaanxi Normal University, People’s Republic of China

Keywords: Primary: 47A53 , Secondary: 47A10 , 47A55 , property (ω) , function of operator , SVEP

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Abstract

Let be an infinite dimensional complex Hilbert space and be the algebra of all bounded linear operators on . For , we say T satisfies property (ω) if σ_a (T) \ σ_ea (T) = π ₀₀(T), where π ₀₀(T) = {λ ∈ isoσ(T) : 0 < n(T − λI) < ∞}. In this paper, we research on the property (ω) for functions of operators by using the new spectrum σ_vea (T) which is a variant of the Weyl essential approximate point spectrum. At the same time, the stability of SVEP as well as the relationships between the two parts is also given.

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