Perturbed Browder, Weyl theorems and their variations: An addendum
Abstract
We generalize some results of Zariouh \cite{Za2} on properties $(\bf{Z}_{\Pi^a})$ and $(\bf{Z}_{E^a})$ from the direct sum $A\oplus B$ (of Banach space operators $A, B$) to upper triangular matrix operators with main diagonal $\{A, B\}$ and answer two questions from \cite{Za2}, one of them affirmatively and the other in the negative.
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bibitem{A} P. Aiena, Fredholm and Local Spectral Theory
with Applications to Multipliers, Kluwer, 2004.
bibitem{BM} M. Berkani and D. Medkova, {em A note on the index of B-Fredholm operators},
Math. Bohemica {bf 29}(2004), 177-180.
bibitem{BS1} M. Berkani and M. Sarih, {em On semi B-Fredholm operators},
Glasgow Math. J. {bf 43}(2001), 457-465.
bibitem{BS2} M. Berkani and M. Sarih, {em An Atkinson-type theorem for B-Fredholm operators},
Studia Math. {bf 148}(2001), 251-257.
bibitem{DDC} B.P. Duggal, S.V. Djordjevic and M. Cho, {em The Browder and Weyl spectra of an operator and its diagonal},
Functional Analysis, Approximation and Computation {bf 1}:2(2009), 7-18.
bibitem{D1} B. P. Duggal, {em Spectral picture, perturbed Browder and Weyl theorems, and their variations}, Functional Analysis, Approximation and Computation {bf 9}:1(2017), 1-23.
bibitem{D2} B. P. Duggal, {em Perturbed Browder and Weyl theorems, and their variations: Equivalences},
Functional Analysis, Approximation and Computation {bf 9}:2(2017), 37-62.
bibitem{Gr} S. Grabiner, {em Uniform ascent and descent of bounded
operators}, J. Math. Soc. Japan {bf 34}(1982), 317-337.
bibitem{H} H. G. Heuser, Functional Analysis, John Wiley and Sons (1982).
bibitem{LN} K.B. Laursen and M.M. Neumann, Introduction to Local Spectral
Theory, Clarendon Press, Oxford, 2000.
bibitem{TL} A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, John Wiley and Sons, 1980.
bibitem{Za1} H. Zariouh, {em On the property $(bf{{Z}_{E_a}})$}, Rend. Mat. Circ. Palermo {bf 65}(2016), 323-331.
bibitem{Za2} H. Zariouh, {em Property $(bf{Z_{E_a}})$ for direct sums}, Functional Analysis, Approximation and Computation {bf 10}:1(2018), 1-7.
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