| Title:
|
Factorization theorem for $1$-summing operators (English) |
| Author:
|
Ferrando, Irene |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
785-793 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study some classes of summing operators between spaces of integrable functions with respect to a vector measure in order to prove a factorization theorem for $1$-summing operators between Banach spaces. (English) |
| Keyword:
|
vector measures |
| Keyword:
|
integrable functions |
| Keyword:
|
sequences on Banach spaces |
| Keyword:
|
summing operators |
| MSC:
|
46E30 |
| MSC:
|
46G10 |
| MSC:
|
47A68 |
| MSC:
|
47B10 |
| MSC:
|
47B47 |
| idZBL:
|
Zbl 1249.47007 |
| idMR:
|
MR2853092 |
| DOI:
|
10.1007/s10587-011-0027-9 |
| . |
| Date available:
|
2011-09-22T14:47:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141639 |
| . |
| Reference:
|
[1] Bartle, R. G., Dunford, N., Schwartz, J.: Weak Compactness and Vector Measures.Canad. J. Math. 7 (1955), 289-305. Zbl 0068.09301, MR 0070050, 10.4153/CJM-1955-032-1 |
| Reference:
|
[2] Blasco, O., Calabuig, J. M., Signes, T.: A bilinear version of Orlicz-Pettis Theorem.J. Math. Anal. Appl. 348 (2008), 150-164. Zbl 1161.46005, MR 2449334, 10.1016/j.jmaa.2008.07.013 |
| Reference:
|
[3] Calabuig, J. M.: Integración bilineal.Tesis doctoral (2004). |
| Reference:
|
[4] Curbera, G. P.: Operators into $L^1$ of a vector measure and applications to Banach lattices.Math. Ann. 293 (1992), 317-330. MR 1166123, 10.1007/BF01444717 |
| Reference:
|
[5] Diestel, J., Jr., J. J. Uhl: Vector Measures.Amer. Math. Soc. Surveys 15, Providence, R.I. (1977). Zbl 0369.46039, MR 0453964 |
| Reference:
|
[6] Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators.Cambridge Studies in Advanced Mathematics, Cambridge (1995). Zbl 0855.47016, MR 1342297 |
| Reference:
|
[7] Ferrando, I., Rodríguez, J.: The weak topology on $L^{p}$ of a vector measure.Topology and its Applications 55 (2008), 1439-1444. MR 2427417 |
| Reference:
|
[8] Lewis, D. R.: Integration with respect to vector measures.Pacific J. Math. 33 (1970), 157-165. Zbl 0195.14303, MR 0259064, 10.2140/pjm.1970.33.157 |
| Reference:
|
[9] Okada, S., Ricker, W., Sánchez-Pérez, E. A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces.Operator Theory: Advances and Applications, Vol. 180, Birkhäuser (2008). MR 2418751 |
| . |
