|
On quasinilpotent operators
Author(s):
Il
Bong
Jung;
Eungil
Ko;
Carl
Pearcy
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2121-2127.
MSC (2000):
Primary 47A15
Posted:
February 5, 2003
MathSciNet review:
1963758
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this note we modify a new technique of Enflo for producing hyperinvariant subspaces to obtain a much improved version of his ``two sequences'' theorem with a somewhat simpler proof. As a corollary we get a proof of the ``best'' theorem (due to V. Lomonosov) known about hyperinvariant subspaces for quasinilpotent operators that uses neither the Schauder-Tychonoff fixed point theorem nor the more recent techniques of Lomonosov.
References:
- [1]
- W. Arveson and J. Feldman, A note on invariant subspaces, Michigan Math. J. 15(1968), 61-64. MR 36:6969
- [2]
- S. Ansari and P. Enflo, Extremal vectors and invariant subspaces, Trans. Amer. Math. Soc. 350(1998), 539-558. MR 98d:47019
- [3]
- N. Aronszajn and K. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. 60(1954), 345-350. MR 16:488b
- [4]
- A. Bernstein and A. Robinson, Solution of an invariant subspace problem of K.T. Smith and P.R. Halmos, Pacific J. Math. 16(1966), 421-431. MR 33:1724
- [5]
- S. Brown, Hyponormal operators with thick spectrum have invariant subspaces, Ann. of Math. 125(1987), 93-103. MR 88c:47010
- [6]
- B. Chevreau, W. Li, and C. Pearcy, A new Lomonosov lemma, J. Operator Theory 40(1998), 409-417. MR 2000b:47014
- [7]
- D. Deckard, R. Douglas, and C. Pearcy, On invariant subspaces of quasitriangular operators, Amer. J. Math. 9(1969), 637-647. MR 41:859
- [8]
- P. Enflo and V. Lomonosov, Some aspects of the invariant subspace problem, preprint.
- [9]
- P. Halmos, Invariant subspaces of polynomially compact operators, Pacific J. Math. 16(1966), 433-437. MR 33:1725
- [10]
- -, Quasitriangular operators, Acta Sci. Math.(Szeged) 29(1968), 283-293. MR 38:2627
- [11]
- V. Lomonosov, On invariant subspaces of families of operators commuting with a completely continuous operator (in Russian), Funkcional Anal. i Prilozen 7(1973), 55-56. MR 54:8319
- [12]
- -, An extension of Burnside's theorem to infinite dimensional spaces, Israel J. Math. 75(1991), 329-339. MR 93h:47007
- [13]
- -, On real invariant subspaces of bounded operators with compact imaginary part, Proc. Amer. Math. Soc. 115(1992), 775-777. MR 92i:47003
- [14]
- C. Pearcy and N. Salinas, An invariant subspace theorem, Michigan Math. J. 20(1973), 21-31. MR 47:5623
- [15]
- C. Pearcy and A. Shields, A survey of the Lomonosov technique in the theory of invariant subspaces, Topics in Operator Theory, Amer. Math. Soc. Surveys, No. 13(1974), 219-229. MR 50:8113
- [16]
- A. Simonic, An extension of Lomonosov's techniques to non-compact operators, Trans. Amer. Math. Soc. 348(1996), 975-995. MR 96j:47005
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
47A15
Retrieve articles in all Journals with
MSC (2000):
47A15
Additional Information:
Il
Bong
Jung
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea
Email:
ibjung@kyungpook.ac.kr
Eungil
Ko
Affiliation:
Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea
Email:
eiko@mm.ewha.ac.kr
Carl
Pearcy
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email:
pearcy@math.tamu.edu
DOI:
10.1090/S0002-9939-03-06895-3
PII:
S 0002-9939(03)06895-3
Keywords:
Invariant subspaces,
Enflo technique,
extremal vectors
Received by editor(s):
February 6, 2002
Posted:
February 5, 2003
Communicated by:
David R. Larson
Copyright of article:
Copyright
2003,
American Mathematical Society
|
