JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS
Yoo, Jong-Kwang;
  PDF(new window)
 Abstract
In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property () on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.
 Keywords
algebraic spectral subspace;analytic spectral subspace;decomposable operator;invariant subspaces property ();property ();subscalar operator;
 Language
English
 Cited by
 References
1.
E. Albrecht, On decomposable operators, Integral Equations Operator Theory 2 (1979), no. 1, 1-10. crossref(new window)

2.
E. Albrecht and J. Eschmeier, Analytic functional models and local spectral theory, Proc. London Math. Soc. (3) 75 (1997), no. 2, 323-348. crossref(new window)

3.
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.

4.
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. crossref(new window)

5.
E. Bishop, A duality theorem for an arbitrary operator, Pacific J. Math. 9 (1959), 375-397.

6.
S. W. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), no. 3, 310-333. crossref(new window)

7.
S. W. Brown, Hyponormal operators with thick spectra have invariant subspaces, Ann. Math. 125 (1987), no. 1, 93-103. crossref(new window)

8.
K. Clancey, Seminormal Operators, Lecture Notes in Math. 742, Springer-Verlag, New York, 1979.

9.
I. Colojoarva and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.

10.
D. Drissi, Local spectrum and Kaplansky's theorem on algebraic operators, Colloq. Math. 75 (1998), no. 2, 159-165. crossref(new window)

11.
I. Erdelyi and W. S. Wang, On strongly decomposable operators, Pacific J. Math. 110 (1984), no. 2, 287-296. crossref(new window)

12.
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. crossref(new window)

13.
E. Ko, k-quasihyponormal operators are subscalar, Integral Equations Operator Theory 28 (1997), no. 4, 492-499. crossref(new window)

14.
R. Lange, A purely analytic criterion for a decomposable operator, Glasgow Math. J. 21 (1980), no. 1, 69-70. crossref(new window)

15.
K. B. Laursen, Algebraic spectral subspaces and automatic continuity, Czechoslovak Math. J. 38(113) (1988), no. 1, 157-172.

16.
K. B. Laursen, Operators with finite ascent, Pacific J. Math. 152 (1992), no. 2, 323-336. crossref(new window)

17.
K. B. Laursen and M. M. Neumann, Decomposable operators and automatic continuity, J. Operator Theory 15 (1986), no. 1, 33-51.

18.
K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon Press Oxford Science Publications, Oxford, 2000.

19.
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.

20.
M. Mbekhta, Generalisation de la decomposition de Kato aux operateurs paranormaux at spectraux, Glasgow Math. J. 29 (1987), no. 2, 159-175. crossref(new window)

21.
M. Mbekhta, Sur la theorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1991), no. 3, 621-631.

22.
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. crossref(new window)

23.
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. crossref(new window)

24.
V. Ptak and P. Vrbova, On the spectral function of a normal operator, Czechoslovak Math. J. 23(98) (1973), 615-616. crossref(new window)

25.
M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385-395.

26.
C. J. Read, Quasinilpotent operators and the invariant subspace problem, J. London Math. Soc. (2) 56 (1997), no. 3, 595-606. crossref(new window)

27.
S. L. Sun, The single-valued extension property and spectral manifolds, Proc. Amer. Math. Soc. 118 (1993), no. 1, 77-87. crossref(new window)

28.
F.-H. Vasilescu, Analytic functional calculus and spectral decompositions, Editura Academiei and D. Reidel Publishing Company, Bucharest and Dordrecht, 1982.

29.
P. Vrbova, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23(98) (1973), 483-492.

30.
P. Vrbova, Structure of maximal spectral spaces of generalized scalar operators, Czechoslovak Math. J. 23(98) (1973), 493-496.

31.
J.-K. Yoo, Local spectral theory for operators on Banach spaces, Far East J. Math. Soc. (2001), Special Vol. Part III, 303-311.