Previous |  Up |  Next


Title: Reflexivity of bilattices (English)
Author: Kliś-Garlicka, Kamila
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 63
Issue: 4
Year: 2013
Pages: 995-1000
Summary lang: English
Category: math
Summary: We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice $\mathcal {L}$ we may associate a bilattice $\Sigma _{\mathcal {L}}$. Similarly, having a bilattice $\Sigma $ we may construct a subspace lattice $\mathcal {L}_{\Sigma }$. Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive. (English)
Keyword: reflexive algebra
Keyword: reflexive lattice
Keyword: subspace lattice
Keyword: bilattice
MSC: 47A15
MSC: 47L99
idZBL: Zbl 06373957
idMR: MR3165510
DOI: 10.1007/s10587-013-0067-4
Date available: 2014-01-28T14:12:12Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] Davidson, K. R., Harrison, K. J.: Distance formulae for subspace lattices.J. Lond. Math. Soc., II. Ser. 39 (1989), 309-323. Zbl 0723.47003, MR 0991664, 10.1112/jlms/s2-39.2.309
Reference: [2] Hadwin, D.: General view of reflexivity.Trans. Am. Math. Soc. 344 (1994), 325-360. Zbl 0802.46010, MR 1239639, 10.1090/S0002-9947-1994-1239639-4
Reference: [3] Halmos, P. R.: Two subspaces.Trans. Am. Math. Soc. 144 (1969), 381-389. Zbl 0187.05503, MR 0251519, 10.1090/S0002-9947-1969-0251519-5
Reference: [4] Loginov, A. I., Shulman, V. S.: Hereditary and intermediate reflexivity of $W^*$-algebras.Izv. Akad. Nauk SSSR, Ser. Mat. 39 (1975), 1260-1273 Russian. MR 0405124
Reference: [5] Sarason, D.: Invariant subspaces and unstarred operator algebras.Pac. J. Math. 17 (1966), 511-517. Zbl 0171.33703, MR 0192365, 10.2140/pjm.1966.17.511
Reference: [6] Shulman, V. S.: Nest algebras by K. R. Davidson: a review.Algebra Anal. 2 (1990), 236-255.
Reference: [7] Shulman, V. S., 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


Files Size Format View
CzechMathJ_63-2013-4_10.pdf 227.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo