A note on the hyperreflexivity constant for certain reflexive algebras

Satoru Tosaka

Studia Mathematica (1999)

  • Volume: 134, Issue: 3, page 203-206
  • ISSN: 0039-3223

Abstract

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Using results on the reflexive algebra with two invariant subspaces, we calculate the hyperreflexivity constant for this algebra when the Hilbert space is two-dimensional. Then by the continuity of the angle for two subspaces, there exists a non-CSL hyperreflexive algebra with hyperreflexivity constant C for every C>1. This result leads to a kind of continuity for the hyperreflexivity constant.

How to cite

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Tosaka, Satoru. "A note on the hyperreflexivity constant for certain reflexive algebras." Studia Mathematica 134.3 (1999): 203-206. <http://eudml.org/doc/216633>.

@article{Tosaka1999,
abstract = {Using results on the reflexive algebra with two invariant subspaces, we calculate the hyperreflexivity constant for this algebra when the Hilbert space is two-dimensional. Then by the continuity of the angle for two subspaces, there exists a non-CSL hyperreflexive algebra with hyperreflexivity constant C for every C>1. This result leads to a kind of continuity for the hyperreflexivity constant.},
author = {Tosaka, Satoru},
journal = {Studia Mathematica},
keywords = {reflexive algebra; invariant subspaces; non-CSL hyperreflexive algebra; hyperreflexivity constant},
language = {eng},
number = {3},
pages = {203-206},
title = {A note on the hyperreflexivity constant for certain reflexive algebras},
url = {http://eudml.org/doc/216633},
volume = {134},
year = {1999},
}

TY - JOUR
AU - Tosaka, Satoru
TI - A note on the hyperreflexivity constant for certain reflexive algebras
JO - Studia Mathematica
PY - 1999
VL - 134
IS - 3
SP - 203
EP - 206
AB - Using results on the reflexive algebra with two invariant subspaces, we calculate the hyperreflexivity constant for this algebra when the Hilbert space is two-dimensional. Then by the continuity of the angle for two subspaces, there exists a non-CSL hyperreflexive algebra with hyperreflexivity constant C for every C>1. This result leads to a kind of continuity for the hyperreflexivity constant.
LA - eng
KW - reflexive algebra; invariant subspaces; non-CSL hyperreflexive algebra; hyperreflexivity constant
UR - http://eudml.org/doc/216633
ER -

References

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  1. [1] M. Anoussis, A. Katavolos and M. S. Lambrou, On the reflexive algebra with two invariant subspaces, J. Operator Theory 30 (1993), 267-299. Zbl0840.47035
  2. [2] W. Argyros, M. S. Lambrou and W. Longstaff, Atomic Boolean subspace lattices and applications to the theory of bases, Mem. Amer. Math. Soc. 445 (1991). Zbl0738.47047
  3. [3] W. Arveson, Ten Lectures on Operator Algebras, CBMS Regional Conf. Ser. in Math. 55, Amer. Math. Soc., Providence, 1984. 
  4. [4] A. Katavolos, M. S. Lambrou and W. Longstaff, The decomposability of operators relative to two subspaces, Studia Math. 105 (1993), 25-36. Zbl0810.47037
  5. [5] M. S. Lambrou and W. Longstaff, Unit ball density and the operator equation AX=YB, J. Operator Theory 25 (1991), 383-397. Zbl0806.47015
  6. [6] M. Papadakis, On hyperreflexivity and rank one density for non-CSL algebras, Studia Math. 98 (1991), 11-17. Zbl0755.47030

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