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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Duality and Kato's theorem on small perturbations


Author: Le Quang Chu
Journal: Bull. Amer. Math. Soc. 82 (1976), 896-898
MSC (1970): Primary 47A55, 47B30
MathSciNet review: 0435898
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  • 1. Marc De Wilde and Le Quang Chu, Perturbation of maps in locally convex spaces, Math. Ann. 215 (1975), 215–233. MR 0473887 (57 #13546)
  • 2. I. C. Gohberg and M. G. Kreĭn, The basic propositions on defect numbers, root numbers and indices of linear operators, Uspehi Mat. Nauk 12 (1957), no. 2 (74), 43—118; English transl., Amer. Math. Soc. Transl. (2) 13 (1960), 185-264. MR 20 #3459; 22 #3984.
  • 3. Tosio Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261–322. MR 0107819 (21 #6541)
  • 4. Le Quang Chu, Bounded perturbations of Φ, Bull. Soc. Roy. Sci. Liège 1-2 (1975), 28-35; addendum, ibid. 9-10 (1975), 537—539; corrigendum, ibid, (to appear).
  • 5. Le Quang Chu, A short proof of Vladimirskii’s theorem on precompact perturbations in locally convex spaces, Canad. Math. Bull. 18 (1975), no. 5, 649–655. MR 0415367 (54 #3455)
  • 6. A. P. Robertson and Wendy Robertson, Topological vector spaces, 2nd ed., Cambridge University Press, London-New York, 1973. Cambridge Tracts in Mathematics and Mathematical Physics, No. 53. MR 0350361 (50 #2854)
  • 7. Ju. N. Vladimirskiĭ, Bounded perturbations of Φ-operators in locally convex spaces, Dokl. Akad. Nauk SSSR 196 (1971), 263–265 (Russian). MR 0273457 (42 #8335)
  • 8. Ju. N. Vladimirskiĭ, Compact perturbations of Φ-operators in locally convex spaces, Sibirsk. Mat. Ž. 14 (1973), 738–759, 909 (Russian). MR 0634980 (58 #30404)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1976-14200-0
PII: S 0002-9904(1976)14200-0