A NOTE ON LINEAR OPERATORS RS AND SR

Jong-Kwang Yoo (Korea)

Received September 30, 2007

References:

[1] P. Aiena, M. L. Colasante and M. Gonzalez, Operators which have a closed quasi-nilpotent part, Proc. Amer. Math. Soc. 130 (2002), 2701-2710. [2] C. Benhida and E. H. Zerouali, Local spectral theory of linear operators RS and SR, Integr. Equ. Oper. Theory 54 (2006), 1-8. [3] E. Bishop, A duality theory for arbitrary operators, Pacific J. Math. 9 (1959), 379-397. [4] L. Chen, Y. Zikun and R. Yingbin, Common properties of operators RS and SR and p-hyponormal operators, Integr. Equ. Oper. Theory 43 (2002), 313-325. [5] I. Colojoarv| and C. Foiás, Theory of Generalized Spectral Operators, Gorden and Breach, New York, 1968. [6] J. K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58(1) (1975), 61-69. [7] K. B. Laursen, Some remarks on automatic continuity, in spaces of analytic functions, Springer Lecture Notes 512 (1976), 96-108. [8] K. B. Laursen, Algebraic spectral subspaces and automatic continuity, Czech. Math. J. 38(113) (1988), 157-172. [9] K. B. Laursen, Intertwining with isometries, Conference on Automatic Continuity and Banach Algebras Canberra (1989), 254-259. [10] K. B. Laursen, Some remarks on the surjectivity spectrum of linear operators, Czech. Math. J. 39 (1989), 730-739. [11] K. B. Laursen, Operators with finite ascent, Pacific J. Math. 152 (1992), 326-336. [12] K. B. Laursen and M. M. Neumann, Decomposable operators and automatic continuity, J. Operator Theory 15 (1986), 33-51. [13] K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon Press, Oxford, 2000. [14] K. B. Laursen and P. Vrbová, Some remarks on the surjectivity spectrum of linear operators, Czech. Math. J. 39(114) (1989), 730-739. [15] M. Mbekhta, Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621-631. [16] V. Pták and P. Vrbová, Algebraic spectral subspaces, Czech. Math. J. 38 (1988), 342-350. [17] P. Vrbová, On local spectral properties of operators in Banach spaces, Czech. Math. J. 23(98) (1973), 483-492.

Keywords and phrases: Dunford’s property (C), property (Q), finite ascent, algebraic spectral subspace, analytic core, quasi-nilpotent part.