Hyperreflexivity of bilattices

Kamila Kliś-Garlicka

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 1, page 119-125
  • ISSN: 0011-4642

Abstract

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The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice ℒ we can construct the bilattice Σ ℒ . Similarly, having a bilattice Σ we may consider the lattice ℒ Σ . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive or not hyperreflexive bilattices are given.

How to cite

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Kliś-Garlicka, Kamila. "Hyperreflexivity of bilattices." Czechoslovak Mathematical Journal 66.1 (2016): 119-125. <http://eudml.org/doc/276759>.

@article{Kliś2016,
abstract = {The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice $\mathcal \{L\}$ we can construct the bilattice $\Sigma _\{\mathcal \{L\}\}$. Similarly, having a bilattice $\Sigma $ we may consider the lattice $\mathcal \{L\}_\{\Sigma \}$. In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive or not hyperreflexive bilattices are given.},
author = {Kliś-Garlicka, Kamila},
journal = {Czechoslovak Mathematical Journal},
keywords = {reflexive bilattice; hyperreflexive bilattice; subspace lattice; bilattice},
language = {eng},
number = {1},
pages = {119-125},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hyperreflexivity of bilattices},
url = {http://eudml.org/doc/276759},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Kliś-Garlicka, Kamila
TI - Hyperreflexivity of bilattices
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 119
EP - 125
AB - The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice $\mathcal {L}$ we can construct the bilattice $\Sigma _{\mathcal {L}}$. Similarly, having a bilattice $\Sigma $ we may consider the lattice $\mathcal {L}_{\Sigma }$. In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples of hyperreflexive or not hyperreflexive bilattices are given.
LA - eng
KW - reflexive bilattice; hyperreflexive bilattice; subspace lattice; bilattice
UR - http://eudml.org/doc/276759
ER -

References

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  1. Arveson, W., 10.1016/0022-1236(75)90041-5, J. Funct. Anal. 20 (1975), 208-233. (1975) MR0383098DOI10.1016/0022-1236(75)90041-5
  2. Davidson, K. R., Harrison, K. J., 10.1112/jlms/s2-39.2.309, J. Lond. Math. Soc., (2) 39 (1989), 309-323. (1989) Zbl0723.47003MR0991664DOI10.1112/jlms/s2-39.2.309
  3. Kli{ś}-Garlicka, K., 10.1007/s10587-013-0067-4, Czech. Math. J. 63 (2013), 995-1000. (2013) Zbl1313.47024MR3165510DOI10.1007/s10587-013-0067-4
  4. Kraus, J., Larson, D. R., 10.1112/plms/s3-53.2.340, Proc. Lond. Math. Soc. (3) 53 (1986), 340-356. (1986) MR0850224DOI10.1112/plms/s3-53.2.340
  5. Shulman, V., Turowska, L., 10.1016/S0022-1236(03)00270-2, J. Funct. Anal. 209 (2004), 293-331. (2004) Zbl1071.47066MR2044225DOI10.1016/S0022-1236(03)00270-2
  6. Shulman, V., A review of "Nest Algebras by K. R. Davidson, Longman Sci. and Techn. Pitman Research Notes Math., 1988", Algebra and Analiz 2 (1990), 236-255 http://www.mathnet.ru/links/04e6653e78d90590f32a76de1b827b3b/aa194.pdf. (1990) 

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