Abstract
It is proved that a wide class of Bishop-type operators Tϕ,τ are power-regular operators in Lp(Ω,μ), 1⩽p<∞, computing the exact value of the local spectral radius at any function u∈Lp(Ω,μ). Moreover, it is shown that the local spectral radius at any u coincides with the spectral radius of Tϕ,τ as far as u is non-zero. As a consequence, it is proved that non-invertible Bishop-type operators are non-decomposable whenever log|ϕ|∈L1(Ω,μ) (in particular, not quasinilpotent); not enjoying even the weaker spectral decompositions \textit{Bishop property} (β) and \textit{property} (δ).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
