# A note on the hyperreflexivity constant for certain reflexive algebras

Studia Mathematica (1999)

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

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topTosaka, 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

top- [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] 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] W. Arveson, Ten Lectures on Operator Algebras, CBMS Regional Conf. Ser. in Math. 55, Amer. Math. Soc., Providence, 1984.
- [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] 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] M. Papadakis, On hyperreflexivity and rank one density for non-CSL algebras, Studia Math. 98 (1991), 11-17. Zbl0755.47030

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