References
- E. Albrecht, On decomposable operators, Integral Equations Operator Theory 2 (1979), no. 1, 1-10. https://doi.org/10.1007/BF01729357
- E. Albrecht and J. Eschmeier, Analytic functional models and local spectral theory, Proc. London Math. Soc. (3) 75 (1997), no. 2, 323-348. https://doi.org/10.1112/S0024611597000373
- E. Albrecht, J. Eschmeier, and M. M. Neumann, Some topics in the theory of decomposable operators, In: Advances in invariant subspaces and other results of Operator Theory: Advances and Applications, 17, Birkhauser Verlag, Basel, 1986.
- C. Benhida and E. H. Zerouali, Local spectral theory of linear operators RS and SR, Integral Equations Operator Theory 54 (2006), no. 1, 1-8. https://doi.org/10.1007/s00020-005-1375-3
- E. Bishop, A duality theorem for an arbitrary operator, Pacific J. Math. 9 (1959), 375-397.
- S. W. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), no. 3, 310-333. https://doi.org/10.1007/BF01682842
- S. W. Brown, Hyponormal operators with thick spectra have invariant subspaces, Ann. Math. 125 (1987), no. 1, 93-103. https://doi.org/10.2307/1971289
- K. Clancey, Seminormal Operators, Lecture Notes in Math. 742, Springer-Verlag, New York, 1979.
- I. Colojoarva and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
- D. Drissi, Local spectrum and Kaplansky's theorem on algebraic operators, Colloq. Math. 75 (1998), no. 2, 159-165. https://doi.org/10.4064/cm-75-2-159-165
- I. Erdelyi and W. S. Wang, On strongly decomposable operators, Pacific J. Math. 110 (1984), no. 2, 287-296. https://doi.org/10.2140/pjm.1984.110.287
-
J. Eschmeier and B. Prunaru, Invariant subspaces for operators with Bishop's property (
$\beta$ ) and thick spectrum, J. Funct. Anal. 94 (1990), no. 1, 196-222. https://doi.org/10.1016/0022-1236(90)90034-I - E. Ko, k-quasihyponormal operators are subscalar, Integral Equations Operator Theory 28 (1997), no. 4, 492-499. https://doi.org/10.1007/BF01309158
- R. Lange, A purely analytic criterion for a decomposable operator, Glasgow Math. J. 21 (1980), no. 1, 69-70. https://doi.org/10.1017/S0017089500003992
- K. B. Laursen, Algebraic spectral subspaces and automatic continuity, Czechoslovak Math. J. 38(113) (1988), no. 1, 157-172.
- K. B. Laursen, Operators with finite ascent, Pacific J. Math. 152 (1992), no. 2, 323-336. https://doi.org/10.2140/pjm.1992.152.323
- K. B. Laursen and M. M. Neumann, Decomposable operators and automatic continuity, J. Operator Theory 15 (1986), no. 1, 33-51.
- K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon Press Oxford Science Publications, Oxford, 2000.
- K. B. Laursen and P. Vrbova, Some remarks on the surjectivity spectrum of linear operators, Czechoslovak Math. J. 39(114) (1989), no. 4, 730-739.
- M. Mbekhta, Generalisation de la decomposition de Kato aux operateurs paranormaux at spectraux, Glasgow Math. J. 29 (1987), no. 2, 159-175. https://doi.org/10.1017/S0017089500006807
- M. Mbekhta, Sur la theorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1991), no. 3, 621-631.
-
T. L. Miller and V. G. Miller, An operator satisfying Dunford's condition (C) but without Bishop's property (
$\beta$ ), Glasgow Math. J. 40 (1998), no. 3, 427-430. https://doi.org/10.1017/S0017089500032754 - T. L. Miller and V. G. Miller, and M. M. Neumann, Spectral subspaces of subscalar and related operators, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1483-1493. https://doi.org/10.1090/S0002-9939-03-07217-4
- V. Ptak and P. Vrbova, On the spectral function of a normal operator, Czechoslovak Math. J. 23(98) (1973), 615-616. https://doi.org/10.1007/BF01593911
- M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385-395.
- C. J. Read, Quasinilpotent operators and the invariant subspace problem, J. London Math. Soc. (2) 56 (1997), no. 3, 595-606. https://doi.org/10.1112/S0024610797005486
- S. L. Sun, The single-valued extension property and spectral manifolds, Proc. Amer. Math. Soc. 118 (1993), no. 1, 77-87. https://doi.org/10.1090/S0002-9939-1993-1156474-0
- F.-H. Vasilescu, Analytic functional calculus and spectral decompositions, Editura Academiei and D. Reidel Publishing Company, Bucharest and Dordrecht, 1982.
- P. Vrbova, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23(98) (1973), 483-492.
- P. Vrbova, Structure of maximal spectral spaces of generalized scalar operators, Czechoslovak Math. J. 23(98) (1973), 493-496.
- J.-K. Yoo, Local spectral theory for operators on Banach spaces, Far East J. Math. Soc. (2001), Special Vol. Part III, 303-311.