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A generalization of Lomonosov's inequality and its applications to invariant subspaces

Author: Shamim I. Ansari
Journal: Proc. Amer. Math. Soc. 130 (2002), 2905-2909
MSC (2000): Primary 47A15
Published electronically: 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.

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  • [G] James Glimm, A Stone-Weierstrass theorem for $C^{*} $-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
  • [L1] 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
  • [Rao] T.S.S.R.K. Rao, A note on extreme points of $WC(K,W)^{*}$, J. Ramanujan Math. Soc. Vol. 9, No. 2 (1994) 215-219. MR 95j:46039

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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

Received by editor(s): December 15, 2000
Published electronically: May 8, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society