| 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:
|
http://hdl.handle.net/10338.dmlcz/143612 |
| . |
| 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 |
| . |
