Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An operator still not satisfying Lomonosov's hypothesis


Author: Don Hadwin
Journal: Proc. Amer. Math. Soc. 123 (1995), 3039-3041
MSC: Primary 47A15; Secondary 47B37
DOI: https://doi.org/10.1090/S0002-9939-1995-1264812-5
MathSciNet review: 1264812
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It was shown that quasianalytic unilateral shifts do not satisfy the hypothesis of a famous invariant subspace theorem of V. Lomonosov. We prove that these same shifts do not satisfy the hypothesis of Lomonosov's recent improvement of his theorem.


References [Enhancements On Off] (What's this?)

  • [C] C. Cowen, An analytic Toeplitz operator that commutes with a compact operator, J. Funct. Anal. 36 (1980), 169-184. MR 569252 (81d:47020)
  • [HNRR] D. Hadwin, E. Nordgren, H. Radjavi, and P. Rosenthal, An operator not satisfying Lomonosov's hypothesis, J. Funct. Anal 38 (1980), 410-415. MR 593088 (81m:47013)
  • [L1] V. Lomonosov, Invariant subspaces for operators commuting with compact operators, Funkcional. Anal, i Priložen 7 (1973), 55-56; English transl., Functional Anal. Appl. 7 (1973), 213-214. MR 0420305 (54:8319)
  • [L2] -, An extension of Burnside's theorem to infinite-dimensional spaces, Israel J. Math. 75 (1991), 329-339. MR 1164597 (93h:47007)
  • [Ru] W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1987. MR 924157 (88k:00002)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A15, 47B37

Retrieve articles in all journals with MSC: 47A15, 47B37


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1264812-5
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society