| Title:
|
U-ideals of factorable operators (English) |
| Author:
|
John, Kamil |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
607-616 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are $u$-ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space. (English) |
| Keyword:
|
factorization of linear operators |
| Keyword:
|
u-ideal |
| Keyword:
|
approximation properties |
| Keyword:
|
unconditional basis |
| MSC:
|
46A32 |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
46B28 |
| MSC:
|
46B99 |
| MSC:
|
46H10 |
| MSC:
|
47L20 |
| idZBL:
|
Zbl 1008.46002 |
| idMR:
|
MR1708346 |
| . |
| Date available:
|
2009-09-24T10:25:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127513 |
| . |
| Reference:
|
[E,J] G. Emmanuele, K. John: Some remarks on the position of the space ${\mathcal K}(X,Y)$ inside the space ${\mathcal W}(X,Y)$.New Zealand J. Math. 26(2) (1997), 183–189. MR 1601639 |
| Reference:
|
[F] J. H. Fourie: Projections on operator duals.Quaestiones Math. 21 (1998), 11–18. Zbl 0938.47020, MR 1658463, 10.1080/16073606.1998.9632022 |
| Reference:
|
[G,K,S] G. Godefroy, N. J. Kalton, P. D. Saphar: Unconditional ideals in Banach spaces.Studia Math. 104 (1) (1993), 13–59. MR 1208038 |
| Reference:
|
[H,W,W] P. Harmand, D. Werner, W. Werner: M-ideals in Banach Spaces and Banach Algebras.Lecture Notes in Math., 1547, Springer, Berlin, 1993. MR 1238713 |
| Reference:
|
[J1] K. John: On the space ${\mathcal K}(P,P^\ast )$ of compact operators on Pisier space P.Note di Matematica 12 (1992), 69–75. MR 1258564 |
| Reference:
|
[J2] K. John: On a result of J. Johnson.Czechoslovak Math. Journal 45 (1995), 235–240. Zbl 0869.46011, MR 1331461 |
| Reference:
|
[Jo] J. Johnson: Remarks on Banach spaces of compact operators.J. Funct. Analysis 32 (1979), 304–311. Zbl 0412.47024, MR 0538857, 10.1016/0022-1236(79)90042-9 |
| Reference:
|
[Ka] N. J. Kalton: Spaces of compact operators.Math. Annalen 208 (1974), 267–278. Zbl 0266.47038, MR 0341154, 10.1007/BF01432152 |
| Reference:
|
[Li] Å. Lima: Property $(wM^*)$ and the unconditional metric approximation property.Studia Math. 113 (3) (1995), 249–263. Zbl 0826.46013, MR 1330210, 10.4064/sm-113-3-249-263 |
| Reference:
|
[LT,I] J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Sequence Spaces.EMG 92 Springer Verlag (1977). MR 0500056 |
| Reference:
|
[LT,II] J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Function Spaces.EMG 97 Springer Verlag (1979). MR 0540367 |
| Reference:
|
[Pie] A. Pietsch: Operator ideals.Berlin, Deutscher Verlag der Wissenschaften, 1978. Zbl 0405.47027, MR 0519680 |
| Reference:
|
[Pi] J. Pisier: Counterexamples to a conjecture of Grothendieck.Acta Mat. 151 (1983), 180–208. Zbl 0542.46038, MR 0723009 |
| Reference:
|
[Ru] W. Ruess: Duality and Geometry of spaces of compact operators.Functional Analysis: Surveys and Recent Results III, Math. Studies 90, North Holland, 1984, pp. 59–78. Zbl 0573.46007, MR 0761373 |
| . |
