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.
@article{bwmeta1.element.bwnjournal-article-smv134i3p203bwm,
author = {Satoru Tosaka},
title = {A note on the hyperreflexivity constant for certain reflexive algebras},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {203-206},
zbl = {0927.47045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv134i3p203bwm}
}
Tosaka, Satoru. A note on the hyperreflexivity constant for certain reflexive algebras. Studia Mathematica, Tome 133 (1999) pp. 203-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv134i3p203bwm/
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