2021/05/05 by Aznay, Zakariae, Zariouh, Hassan
#47A10 #47A11 #47A53 #FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2105.02131
It is well known that an hyponormal operator satisfies Weyl's theorem. A result due to Conway shows that the essential spectrum of a normal operator N consists precisely of all points in its spectrum except the isolated eigenvalues of finite multiplicity, that's σe(N)=σ(N)∖ E0(N). In this paper, we define and study a new class named (We) of operators satisfying σe(T)=σ(T)∖ E0(T), as a subclass of (W). A countrexample shows generally that an hyponormal does not belong to the class (We), and we give an additional hypothesis under which an hyponormal belongs to the class (We). We also give the generalisation class (gWe) in the contexte of B-Fredholm theory, and we characterize (Be), as a subclass of (B), in terms of localized SVEP.