Dissymmetric bilateral weighted shifts are hyper-reflexive

Xavier Dussau

Bulletin de la Société Mathématique de France (2002)

  • Volume: 130, Issue: 4, page 573-585
  • ISSN: 0037-9484

Abstract

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We prove the hyper-reflexivity of the bilateral weighted shift S ω on  ℓ ω 2 ( ℤ ) , when the weight satisfies ω ( n ) = 1 for n ≥ 0 , and lim n → - ∞ ω ( n ) = + ∞ .

How to cite

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Dussau, Xavier. "Les shifts à poids dissymétriques sont hyper-réflexifs." Bulletin de la Société Mathématique de France 130.4 (2002): 573-585. <http://eudml.org/doc/272369>.

@article{Dussau2002,
abstract = {Nous prouvons l’hyper-réflexivité du shift bilatéral $S_\{\omega \}$ sur $\ell _\{\omega \}^\{2\}(\{\mathbb \{Z\}\})$, lorsque le poids vérifie $\omega (n)=1$ for $n \ge 0$ et $\lim _\{n \rightarrow -\infty \}\omega (n)=+\infty $.},
author = {Dussau, Xavier},
journal = {Bulletin de la Société Mathématique de France},
keywords = {weighted shift; reflexivity},
language = {fre},
number = {4},
pages = {573-585},
publisher = {Société mathématique de France},
title = {Les shifts à poids dissymétriques sont hyper-réflexifs},
url = {http://eudml.org/doc/272369},
volume = {130},
year = {2002},
}

TY - JOUR
AU - Dussau, Xavier
TI - Les shifts à poids dissymétriques sont hyper-réflexifs
JO - Bulletin de la Société Mathématique de France
PY - 2002
PB - Société mathématique de France
VL - 130
IS - 4
SP - 573
EP - 585
AB - Nous prouvons l’hyper-réflexivité du shift bilatéral $S_{\omega }$ sur $\ell _{\omega }^{2}({\mathbb {Z}})$, lorsque le poids vérifie $\omega (n)=1$ for $n \ge 0$ et $\lim _{n \rightarrow -\infty }\omega (n)=+\infty $.
LA - fre
KW - weighted shift; reflexivity
UR - http://eudml.org/doc/272369
ER -

References

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  1. [1] H. Bercovici, C. Foias & B. S. Nagy – « Reflexive and hyper-reflexive operators of class C 0 », Acta Sci. Math (Szeged) 43 (1981), p. 5–13. Zbl0466.47009MR621348
  2. [2] R. Douglas, H. Shapiro & A. Shields – « Cyclic vectors and invariant subspaces for the backward shift operator », Ann. Inst. Fourier20 (1970), p. 37–76. Zbl0186.45302MR270196
  3. [3] X. Dussau – « Les shifts à poids de croissance polynomiale sont hyper-réflexifs », à paraître. Zbl1053.47027
  4. [4] J. Esterle – « Apostol’s bilateral weighted shifts are hypereflexives », Operator Theory : Advances and Applications, à paraître. Zbl0994.47009
  5. [5] —, « Uniqueness, strong forms of uniqueness and negative powers of contractions », Funct. Anal. and Operator Theory, Banach Center Pub. 30 (1994), p. 127–145. Zbl0893.46043MR1285603
  6. [6] —, « Singular inner functions and biinvariant subspaces for disymmetric weighted shifts », J. Funct. Anal. 144 (1997), no. 1, p. 60–104. Zbl0938.47003MR1430716
  7. [7] V. Kapustin – « Reflexivity of operators : general methods and a criterion for almost isometric contractions », St. Petersbourg Math. J. 4 (1993), no. 2, p. 319–335. Zbl0791.47037MR1182398
  8. [8] B. S. Nagy & C. Foias – Harmonic analysis of operators on Hilbert spaces, North-Holland Publishing. Co., Amsterdam, 1970. Zbl0201.45003MR275190
  9. [9] A. Shields – « Weighted shift operators and analytic function theory », Topics in Operator Theory, Math. Surveys, vol. 13, Amer. Math. Society, Providence, R.I., 1974, p. 49–128. Zbl0303.47021MR361899

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