참고문헌
- P. Aiena, Fredholm and local spectral theory, with application to multipliers, Kluwer Acad. Publishers, 2004.
- P. Aiena and M. T. Biondi, Ascent, descent, quasi-nilpotent part and analytic core of operators, 54 (2002), no. 3-4, 57-70.
- P. Aiena, M. L. Colasante and M. Gonzalez, Operators which have a closed quasinilpotent part, Proc. Amer. Math. Soc. 130 (2002), 2701-2710. https://doi.org/10.1090/S0002-9939-02-06386-4
- E. Albrecht, On two questions of I. Colojoara and C. Foias, Manuscripta Math. 25 (1978), 1-15. https://doi.org/10.1007/BF01170354
- E. Albrecht, On decomposable operators, Integral Equations Operator Theory 2 (1979), 1-10. https://doi.org/10.1007/BF01729357
- E. Albrecht and J. Eschmeier, Analytic fuctional models and local spectral theory, Proc. London Math. Soc. (3) 75 (1997), 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, Birkhauser Verlag, Basel 17 (1986), 15-34.
- S. Ansari and P. Enflo, Extremal vectors and invariant subspaces, Trans. Amer. Math. Soc. 350 (1998), no. 2, 539-558. https://doi.org/10.1090/S0002-9947-98-01865-0
- W. B. Arveson, Ten Lectures on Operator Algebras, vol 55, CBMS Reg. Conf. Ser. Math., Amer. Math. Soc., Providence, RI, 1984.
- Y. A. Abramovitch and C. D. Aliprantis, Positive operators, in: Handbook of the Geometry of Banach spaces, vol. 1, North-Holland, 2001, 85-122.
- N. Aronszajn and K. T. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. 2 (1954), 345-350.
- W. B. Arveson and J. Feldman, A note on invariant subspaces, vol. 15, Michiigan Math. J., (1968), 61-64. https://doi.org/10.1307/mmj/1028999905
- W. G. Bade, P. C. Curtis and K. B. Laursen, Divisible subspaces and problems of automatic continuity, Studia. Math. 68 (1980), 159-186. https://doi.org/10.4064/sm-68-2-159-186
- B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North-Holland Math. Library 42, 1988.
- C. Benhida and E. H. Zerouali, Local spectral theory of linear operators RS and SR, Integral Equations Operator Theory 54 (2006), 1-8. https://doi.org/10.1007/s00020-005-1375-3
- H. Bercovici, C. Foias and C. Pearcy, Dual Algebras with Applications to Invariant Subspaces and Dilation Theory, CBMS Reg. Conf. Ser. Math., vol. 56, Amer. Math. Soc., Providence, RI, 1985.
- A. R. Bernstein and A. Ronbinson, Solution of an invariant subspace problem of K.T. Smith and P.R. Halmose, Pacific J. Math. 16 (1966), 421-431. https://doi.org/10.2140/pjm.1966.16.421
- 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 and 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), 93-103. https://doi.org/10.2307/1971289
- K. Clancey, Seminormal Operators, Lecture Notes in Math., vol. 742, Springer-Verlag, Berlin, 1979.
- I. Colojoarva and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
- P. C. Curtis, Jr. and M. M. Neumann, Non-analytic functional calculi and spectral maximal spaces, Pacific J. Math. 137 (1989), 65-85. https://doi.org/10.2140/pjm.1989.137.65
-
M. Didas,
${\varepsilon}(T^{n})$ -subscalar n-tuples and the Cesaro operator on${H^{p}}$ , Annales Universitatis Saraviensis, Series Mathematicae 10 (2000), 285-335. - N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. https://doi.org/10.2140/pjm.1954.4.321
- N. Dunford and J. T. Schwartz, Linear operators, Part III, Wiley-Interscience, New York, 1971.
- P. Enflo and V. Lomonosov, Some aspects of the invariant subspace problem, in: Handbook of the Geometry of Banach Spaces, vol. 1, 2001, 533-558.
- I. Erdelyi and R. Lange, Spectral decompositions on Banach spaces, Lecture Notes in Mathematics, No. 623, Springer-Verlag, 1977.
- J. Eschmeier, K. B. Laursen and M. M. Neumann, Multipliers with natural local spectra on commutative Banach algebras, J. Functional Analysis 138 (1996), 273-294. https://doi.org/10.1006/jfan.1996.0065
-
J. Eschmeier and B. Prunaru, Invariant subspaces for operators with Bishop's property (
${\beta}$ ) and thick spectrum, J. Functional Anal. 94 (1990), 196-222. https://doi.org/10.1016/0022-1236(90)90034-I -
J. Eschmeier and M. Putinar, Bishop's property (
${\beta}$ ) and rich extensions of linear operators, Indiana Univ. Math. J. 37 (1988), 325-348. https://doi.org/10.1512/iumj.1988.37.37016 - S. Frunza, A characterization of regular Banach algebras, Rev. Roum. Math. Pures Appl. 18 (1973), 1057-1059.
- P. R. Halmos, Invariant subspaces of polynomially compact operators, Pacific J. Math. 16 (1966), 433-437. https://doi.org/10.2140/pjm.1966.16.433
- P. R. Halmos, Invariant subspaces, in: Abstract Spaces and Approximation, Proc. Conf., Oberwolfach, 1968, 1969, 26-30.
- N. D. Hooker , Lomonosov's hyperinvariant subspace theorem for real spaces, Math. Proc. Cambridge Philos. Soc. 89(1) (1981), 129-133. https://doi.org/10.1017/S0305004100058011
- B. E. Johnshon and A. M. Sinclair, Continuity of linear operators commuting with linear operators II, Trans. Amer. Math. Soc. 146 (1969), 533-540. https://doi.org/10.1090/S0002-9947-1969-0251564-X
- Eungil Ko, k-quasihyponormal operators are subscalar, Integral Equations Operator Theory 28 (1997), 492-499. https://doi.org/10.1007/BF01309158
- R. Lange, On generalization of decomposability, Glasgow Math. J. 22 (1981), 77-81. https://doi.org/10.1017/S0017089500004493
- K. B. Laursen, Operators with finite ascent, Pacific J. Math. 152 (1992), 326-336.
- K. B. Laursen and M. M. Neumann, Decomposable operators and automatic continuity, J. Operator Theory 15 (1986), 33-51.
- K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon Press, Oxford Science Publications, Oxford, 2000.
- V. I. Lomonosov, Inariant subspaces of the family of operators that commute with a completely continuous operator, Funkcional. Anal. i Prilonzhen. 7(3) (1973) 55-56 (in Russian); translated in Funct. Anal Appl. 7 (1973), no. 3, 213-214.
- C. E. Rickart, General thoery of Banach algebras, Von Nostrand, Princeton, NJ., 1960.
- M. Mbekhta, Sur la theorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 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), 427-430. https://doi.org/10.1017/S0017089500032754 - T. L. Miller, V. G. Miller and M. M. Neumann, Spectral subspaces of subscalar and related operators, Proc. Amer. Math. Soc. 132 (2004), 1483-1493. https://doi.org/10.1090/S0002-9939-03-07217-4
- M. M. Neumann, Commutative Banach algebras and decomposable operators, Mh. Math. 113 (1992), 227 - 243. https://doi.org/10.1007/BF01641770
- C. Pearcy and N. Salinas, An invarinat-subspace theorem, Michigan Math. J. 20 (1973), 21-31. https://doi.org/10.1307/mmj/1029001007
- 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), 385-395.
- H. Radjavi and P. Rosenthal, Invariant subspaces, Ergeb. Math. Grenzgeb., vol. 77, Springer-Verlag, New York, 1973.
- C. J. Read, Quasinilpotent operators and the invariant subspace problem, J. London Math. Soc. (2) 56 (1997), 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, Structure of maximal spectral spaces of generalized scalar operators, Czechoslovak Math. J. 23(98) (1973), 493-496.
- P. Vrbova, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23(98) (1973), 483-492.