Generalized Weyl's theorem and quasi-affinity (Q2910024)

Let \(X\) and \(Y\) be Banach spaces and \(L(X,Y)\) denote the space of all bounded linear operators from \(X\) to \(Y\). In the first part of the paper, the authors prove that generalized Weyl's theorem holds for several classes of operators, extending results obtained by \textit{R. E. Curto} and \textit{Y. M. Han} [J. Math. Anal. Appl. 336, No.~2, 1424--1442 (2007; Zbl 1131.47003)] and \textit{V. Istrăţescu} [Rev. Roum. Math. Pures Appl. 13, 1103--1105 (1968; Zbl 0175.13602)]. In the second part, the authors study the problem of preserving generalized Weyl's theorem from bounded operators \(S\in L(Y)\) and \(T\in L(X)\) whenever \(S\) and \(T\) are intertwined by a quasi affinity or quasi similarity. At the end, the authors study the preservation of generalized Weyl's theorem from bounded operators \(S\in L(Y)\) and \(T\in L(X)\) in a more general case, whenever \(S\) and \(T\) are asymptotically intertwined by a quasi affinity or asymptotical similarity.NEWLINENEWLINEEditor's remark. The authors have published a paper with the same title in [Stud. Math. 198, No.~2, 105--120 (2010; Zbl 1192.47004)].