A+ CATEGORY SCIENTIFIC UNIT

Stable invariant subspaces for operators on Hilbert space

Volume 66 / 1997

John Conway, Don Hadwin Annales Polonici Mathematici 66 (1997), 49-61 DOI: 10.4064/ap-66-1-49-61

Abstract

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.

Authors

  • John Conway
  • Don Hadwin

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