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1997 | 66 | 1 | 49-61
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Stable invariant subspaces for operators on Hilbert space

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EN
If T is a bounded operator on a separable complex Hilbert space ℋ, an invariant subspace ℳ for T is stable provided that whenever ${T_n}$ is a sequence of operators such that $‖T_n - T‖ → 0$, there is a sequence of subspaces ${ℳ_n}$, with $ℳ_n$ in $Lat T_n$ for all n, such that $P_{ℳ_n} → P_{ℳ}$ in the strong operator topology. If the projections converge in norm, ℳ is called a norm stable invariant subspace. This paper characterizes the stable invariant subspaces of the unilateral shift of finite multiplicity and normal operators. It also shows that in these cases the stable invariant subspaces are the strong closure of the norm stable invariant subspaces.
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Twórcy
  • Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300, U.S.A.
autor
  • Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824, U.S.A.
Bibliografia
  • [1] G. T. Adams, A nonlinear characterization of stable invariant subspaces, Integral Equations Operator Theory 6 (1983), 473-487.
  • [2] C. Apostol, L. A. Fialkow, D. A. Herrero, and D. Voiculescu, Approximation of Hilbert Space Operators, Vol. II, Pitman Res. Notes Math. 102, Pitman, Boston, 1984.
  • [3] C. Apostol, C. Foiaş, and N. Salinas, On stable invariant subspaces, Integral Equations Operator Theory 8 (1985), 721-750.
  • [4] H. Bart, I. Gohberg, and M. A. Kaashoek, Stable factorizations of monic matrix polynomials and stable invariant subspaces, Integral Equations Operator Theory 1 (1978), 496-517.
  • [5] S. Campbell and J. Daughtry, The stable solutions of quadratic matrix equations, Proc. Amer. Math. Soc. 74 (1979), 19-23.
  • [6] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1990.
  • [7] J. B. Conway and P. R. Halmos, Finite-dimensional points of continuity of Lat, Linear Algebra Appl. 31 (1980), 93-102.
  • [8] Yu. P. Ginzburg, The factorization of analytic matrix functions, Dokl. Akad. Nauk SSSR 159 (3) (1964), 489-492 (in Russian).
  • [9] D. W. Hadwin, An addendum to limsups of lats, Indiana Univ. Math. J. 29 (1980), 313-319.
  • [10] P. R. Halmos, Limsups of lats, Indiana Univ. Math. J., 293-311.
  • [11] D. A. Herrero, Inner functions under uniform topology, II, Rev. Un. Mat. Argentina 28 (1976), 23-35.
  • [12] D. A. Herrero, Approximation of Hilbert Space Operators, I, Pitman, London, 1982.
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Bibliografia
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