| Title:
|
The associated tensor norm to $(q,p)$-absolutely summing operators on $C(K)$-spaces (English) |
| Author:
|
López Molina, J. A. |
| Author:
|
Sánchez-Pérez, E. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
627-631 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give an explicit description of a tensor norm equivalent on $C(K) \otimes F$ to the associated tensor norm $\nu _{qp}$ to the ideal of $(q,p)$-absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to $\nu _{qp}$. (English) |
| MSC:
|
46B28 |
| MSC:
|
46M05 |
| MSC:
|
47B07 |
| MSC:
|
47B10 |
| MSC:
|
47L05 |
| MSC:
|
47L20 |
| idZBL:
|
Zbl 0903.46017 |
| idMR:
|
MR1479309 |
| . |
| Date available:
|
2009-09-24T10:09:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127383 |
| . |
| Reference:
|
[1] A. Defant, K. Floret: Tensor norms and Operator Ideals.North-Holland Mathematics Studies 176. Amsterdam-London-New York-Tokyo, 1993. MR 1209438 |
| Reference:
|
[2] J. T. Lapresté: Operateurs sommantes et factorization à travers les espaces $L^p$.Studia Math. 56 (1976), 47–83. MR 0454704 |
| Reference:
|
[3] J. A. López Molina, E. A. Sánchez Pérez: Ideales de operadores absolutamente continuos.Rev. Real Acad. Ciencias Exactas, Fisicas y Naturales, Madrid 87 (1993), 349–378. MR 1318866 |
| Reference:
|
[4] U. Matter: Absolutely continuous operators and super-reflexivity.Math. Nachr. 130 (1987), 193–216. Zbl 0622.47045, MR 0885628, 10.1002/mana.19871300118 |
| Reference:
|
[5] U. Matter, H. Jarchow: Interpolative constructions for operator ideals.Note di Matematica VIII (1988), no. 1, 45–56. MR 1050508 |
| Reference:
|
[6] B. Maurey: Sur certaines propriétés des opérateurs sommants.C. R. Acad. Sci. Paris A 277 (1973), 1053–1055. Zbl 0269.47014, MR 0385621 |
| Reference:
|
[7] A. Pietsch: Operator Ideals.North-Holland Publ. Company, Amsterdam-New York-Oxford, 1980. Zbl 0455.47032, MR 0582655 |
| Reference:
|
[8] G. Pisier: Factorization of operators through $L_{p,\infty }$ or $L_{p,1}$ and non-commutative generalizations.Math. Ann. 276 (1986), 105–136. MR 0863711, 10.1007/BF01450929 |
| . |
