| Title:
|
Pták's characterization of reflexivity in tensor products (English) |
| Author:
|
John, Kamil |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
923-931 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize the reflexivity of the completed projective tensor products $X{\widetilde{\otimes }_\pi } Y$ of Banach spaces in terms of certain approximative biorthogonal systems. (English) |
| Keyword:
|
reflexive Banach space |
| Keyword:
|
biorthogonal system |
| Keyword:
|
$\pi $-tensor product |
| MSC:
|
46B10 |
| MSC:
|
46B28 |
| idZBL:
|
Zbl 1164.46308 |
| idMR:
|
MR2261664 |
| . |
| Date available:
|
2009-09-24T11:39:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128117 |
| . |
| Reference:
|
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| Reference:
|
[2] A. Grothendieck: Produits tensoriels topologiques et espaces nucléaires.Mem. Am. Math. Soc. 16 (1955). Zbl 0123.30301, MR 0075539 |
| Reference:
|
[3] S. Heinrich: On the reflexivity of the Banach space $L(X,Y)$.Funkcional’nyi Analiz i ego Prilozheniya 8 (1974), 97–98. MR 0342991 |
| Reference:
|
[4] J. R. Holub: Reflexivity of $L(E,F)$.Proc. Amer. Math. Soc. 39 (1973), 175–177. Zbl 0262.46015, MR 0315407 |
| Reference:
|
[5] H. Jarchow: Locally Convex Spaces.Teubner-Verlag, Stuttgart, 1981. Zbl 0466.46001, MR 0632257 |
| Reference:
|
[6] K. John: $w^*$-basic sequences and reflexivity of Banach spaces.Czechoslovak Math. J 55 (2005), 677–681. Zbl 1081.46017, MR 2153091, 10.1007/s10587-005-0054-5 |
| Reference:
|
[7] W. B. Johnson, H. P. Rosenthal: On w$^*$ basic sequences and their applications to the study of Banach spaces.Studia Math. 43 (1972), 77–92. MR 0310598, 10.4064/sm-43-1-77-92 |
| Reference:
|
[8] G. Köthe: Topological Vector Spaces II.Springer-Verlag, Berlin-Heidelberg-New York, 1984. MR 0551623 |
| Reference:
|
[9] A. Pełczyński: A note on the paper of I. Singer “Basic sequences and reflexivity of Banach spaces”.Studia Math. 21 (1962), 371–374. MR 0146636, 10.4064/sm-21-3-370-374 |
| Reference:
|
[10] V. Pták: Biorthogonal systems and reflexivity of Banach spaces.Czechoslovak Math. J. 9 (1959), 319–325. MR 0110008 |
| Reference:
|
[11] W. Ruckle: Reflexivity of $L(E,F)$.Proc. Amer. Math. Soc. 34 (1972), 171–174. Zbl 0242.46018, MR 0291777 |
| Reference:
|
[12] W. Ruess: Duality and geometry of spaces of compact operators.In: Functional Analysis: Surveys and Recent Results III. Math. Studies 90, North Holland, , 1984. Zbl 0573.46007, MR 0761373 |
| Reference:
|
[13] I. Singer: Basic sequences and reflexivity of Banach spaces.Studia Math. 21 (1962), 351–369. Zbl 0114.30903, MR 0146635, 10.4064/sm-21-3-351-369 |
| Reference:
|
[14] I. Singer: Bases in Banach Spaces, Vol. I.Springer-Verlag, Berlin-Heidelberg-New York, 1970. MR 0298399 |
| . |
