# Stable invariant subspaces for operators on Hilbert space

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 49-61
- ISSN: 0066-2216

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topJohn B. Conway, and Don Hadwin. "Stable invariant subspaces for operators on Hilbert space." Annales Polonici Mathematici 66.1 (1997): 49-61. <http://eudml.org/doc/269992>.

@article{JohnB1997,

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.},

author = {John B. Conway, Don Hadwin},

journal = {Annales Polonici Mathematici},

keywords = {invariant subspace; stability; normal operators; strong operator topology; norm stable invariant subspace; unilateral shift of finite multiplicity},

language = {eng},

number = {1},

pages = {49-61},

title = {Stable invariant subspaces for operators on Hilbert space},

url = {http://eudml.org/doc/269992},

volume = {66},

year = {1997},

}

TY - JOUR

AU - John B. Conway

AU - Don Hadwin

TI - Stable invariant subspaces for operators on Hilbert space

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 49

EP - 61

AB - 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.

LA - eng

KW - invariant subspace; stability; normal operators; strong operator topology; norm stable invariant subspace; unilateral shift of finite multiplicity

UR - http://eudml.org/doc/269992

ER -

## References

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- [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. Zbl0457.47010
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