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Title: Hyperreflexivity of bilattices (English)
Author: Kliś-Garlicka, Kamila
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 66
Issue: 1
Year: 2016
Pages: 119-125
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: reflexive bilattice
Keyword: hyperreflexive bilattice
Keyword: subspace lattice
Keyword: bilattice
MSC: 47A15
MSC: 47L99
idZBL: Zbl 06587878
idMR: MR3483227
DOI: 10.1007/s10587-016-0244-3
Date available: 2016-04-07T14:59:54Z
Last updated: 2020-07-03
Stable URL:
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Reference: [3] Kli{ś}-Garlicka, K.: Reflexivity of bilattices.Czech. Math. J. 63 (2013), 995-1000. Zbl 1313.47024, MR 3165510, 10.1007/s10587-013-0067-4
Reference: [4] Kraus, J., Larson, D. R.: Reflexivity and distance formulae.Proc. Lond. Math. Soc. (3) 53 (1986), 340-356. MR 0850224, 10.1112/plms/s3-53.2.340
Reference: [5] Shulman, V., Turowska, L.: Operator synthesis. I. Synthetic sets, bilattices and tensor algebras.J. Funct. Anal. 209 (2004), 293-331. Zbl 1071.47066, MR 2044225, 10.1016/S0022-1236(03)00270-2
Reference: [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


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