| Title:
|
The almost lattice isometric copies of $c_0$ in Banach lattices (English) |
| Author:
|
Chen, Jinxi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
409-412 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper it is shown that if a Banach lattice $E$ contains a copy of $c_{0}$, then it contains an almost lattice isometric copy of $c_{0}$. The above result is a lattice version of the well-known result of James concerning the almost isometric copies of $c_{0}$ in Banach spaces. (English) |
| Keyword:
|
Banach lattice |
| Keyword:
|
lattice isometry |
| Keyword:
|
almost lattice isometry |
| Keyword:
|
copy of $c_{0}$ |
| MSC:
|
46B04 |
| MSC:
|
46B25 |
| MSC:
|
46B42 |
| idZBL:
|
Zbl 1123.46010 |
| idMR:
|
MR2174520 |
| . |
| Date available:
|
2009-05-05T16:52:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119536 |
| . |
| Reference:
|
[1] Aliprantis C.D., Burkinshaw O.: Positive Operators.Academic Press, New York, 1985. Zbl 1098.47001, MR 0809372 |
| Reference:
|
[2] Diestel J.: Sequences and Series in Banach Spaces.Springer, New York, 1984. MR 0737004 |
| Reference:
|
[3] Hudzik H., Mastylo M.: Almost isometric copies of $l^{\infty}$ in some Banach spaces.Proc. Amer. Math. Soc. 119 (1993), 209-215. MR 1146861 |
| Reference:
|
[4] Hudzik H.: Banach lattices with order isometric copies of $l^{\infty}$.Indag. Math. (N.S.) 9 (1998), 521-527. MR 1691991 |
| Reference:
|
[5] James R.C.: Uniformly non-square Banach spaces.Ann. of Math. (2) 80 (1964), 542-550. Zbl 0132.08902, MR 0173932 |
| Reference:
|
[6] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I.North-Holland, Amsterdam-London, 1971. |
| Reference:
|
[7] Meyer-Nieberg P.: Banach Lattices.Springer, Berlin-Heidelberg, 1991. Zbl 0743.46015, MR 1128093 |
| . |
