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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Most similarity orbits are strongly dense


Authors: D. W. Hadwin, E. A. Nordgren, Heydar Radjavi and Peter Rosenthal
Journal: Proc. Amer. Math. Soc. 76 (1979), 250-252
MSC: Primary 47A65; Secondary 47A15
MathSciNet review: 537082
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Abstract: It is shown that the strong and weak closures of the similarity orbit of an operator on a Banach space always coincide, and a simple characterization of these closures is given. Whenever an operator is not the sum of a scalar and a finite rank operator, its similarity orbit is strongly dense in the set of all bounded linear operators.


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  • [E] P. Enflo, On the invariant subspace problem in Banach spaces, Séminaire Maurey–Schwartz (1975–1976) Espaces 𝐿^{𝑝}, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. 14-15, Centre Math., École Polytech., Palaiseau, 1976, pp. 7. MR 0473871 (57 #13530)
  • [H1] Donald W. Hadwin, An operator-valued spectrum, Indiana Univ. Math. J. 26 (1977), no. 2, 329–340. MR 0428089 (55 #1118)
  • [H2] -, Approximate equivalence and completely positive maps, preprint, 1978.
  • [HNRR] D. W. Hadwin, E. Nordgren, Heydar Radjavi and Peter Rosenthal, An operator not satisfying Lomonosov's hypothesis, preprint, 1978.
  • [PRH1] P. R. Halmos, Irreducible operators, Michigan Math. J. 15 (1968), 215–223. MR 0231233 (37 #6788)
  • [PRH2] Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368 (34 #8178)
  • [He1] Domingo A. Herrero, Closure of similarity orbits of Hilbert space operators. III, Math. Ann. 232 (1978), no. 3, 195–204. MR 0512775 (58 #23695c)
  • [He2] -, Closure of similarity orbits of Hilbert space operators. V. Essentially BQT operators (preprint).
  • [V] Dan Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113. MR 0415338 (54 #3427)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0537082-1
PII: S 0002-9939(1979)0537082-1
Keywords: Banach space, operator, similarity orbit, weak and strong operator topologies, finite rank operator
Article copyright: © Copyright 1979 American Mathematical Society