| 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:
|
http://hdl.handle.net/10338.dmlcz/144884 |
| . |
| Reference:
|
[1] Arveson, W.: Interpolation problems in nest algebras.J. Funct. Anal. 20 (1975), 208-233. MR 0383098, 10.1016/0022-1236(75)90041-5 |
| Reference:
|
[2] Davidson, K. R., Harrison, K. J.: Distance formulae for subspace lattices.J. Lond. Math. Soc., (2) 39 (1989), 309-323. Zbl 0723.47003, MR 0991664, 10.1112/jlms/s2-39.2.309 |
| 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 http://www.mathnet.ru/links/04e6653e78d90590f32a76de1b827b3b/aa194.pdf. |
| . |
