A note on the common spectral properties for bounded linear operators

2019/03/26 by Zguitti, Hassane
#47A10 #47A53 #47A55 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1903.11153

Abstract

Let X and Y be Banach spaces, A : X→ Y and B, C : Y→ X be bounded linear operators. We prove that if A(BA)²=ABACA=ACABA=(AC)²A, then σ_*(AC)∖\0\=σ_*(BA)∖\0\ where σ_* runs over a large of spectra originated by regularities.

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