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A generalization of Lomonosov's inequality and its applications to invariant subspaces
Author(s):
Shamim
I.
Ansari
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2905-2909.
MSC (2000):
Primary 47A15
Posted:
May 8, 2002
MathSciNet review:
1908913
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Abstract:
In this article we generalize Victor Lomonosov's famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.
References:
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- James Glimm, A Stone-Weierstrass theorem for
 -algebras, Ann. of Math. (2) 72 1960 216-244. MR 22:7005 - [H1]
- Don Hadwin, A reflexivity theorem for subspaces of Calkin algebras, J. Funct. Anal. 123 (1994), no. 1, 1-11. MR 96b:47054
- [H2]
- Don Hadwin, An operator still not satisfying Lomonosov's hypothesis, Proc. Amer. Math. Soc. 123 (1995), no. 10, 3039-3041. MR 95m:47006
- [I]
- Vasile I. Istratescu, Strict convexity and complex strict convexity. Theory and applications, Lecture Notes in Pure and Applied Mathematics, 89. Marcel Dekker, Inc., New York, 1984. MR 86b:46023
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- Victor Lomonosov, Invariant subspaces of the family of operators that commute with a completely continuous operator, (Russian) Funkcional. Anal. i Prilozen. 7 (1973), no. 3, 55-56. MR 54:8319
- [L2]
- Victor Lomonosov, An Extension of Burnside's Theorem to Infinite Dimensional Spaces, Israel Journal of Mathematics, 75, (1991) 329-339. MR 93h:47007
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Additional Information:
Shamim
I.
Ansari
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, P.O. Box MA, Mississippi State, Mississippi 39762
Email:
shmansr@aol.com
DOI:
10.1090/S0002-9939-02-06644-3
PII:
S 0002-9939(02)06644-3
Received by editor(s):
December 15, 2000
Posted:
May 8, 2002
Communicated by:
David R. Larson
Copyright of article:
Copyright
2002,
American Mathematical Society
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