| Title:
|
On an inclusion between operator ideals (English) |
| Author:
|
Fugarolas, Manuel A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
209-212 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $ 1\leq q <p < \infty $ and $1/r := 1/p \max (q/2, 1)$. We prove that ${\scr L}_{r,p}^{(c)}$, the ideal of operators of Geľfand type $l_{r,p}$, is contained in the ideal $\Pi _{p,q}$ of $(p,q)$-absolutely summing operators. For $q>2$ this generalizes a result of G. Bennett given for operators on a Hilbert space. (English) |
| Keyword:
|
operator ideals |
| Keyword:
|
$s$-numbers |
| MSC:
|
47B06 |
| MSC:
|
47B10 |
| MSC:
|
47L20 |
| idZBL:
|
Zbl 1216.47110 |
| idMR:
|
MR2782769 |
| DOI:
|
10.1007/s10587-011-0007-0 |
| . |
| Date available:
|
2011-05-23T12:42:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141528 |
| . |
| Reference:
|
[1] Bennett, G.: Some ideals of operators on Hilbert space.Studia Math. 55 (1976), 27-40. Zbl 0338.47013, MR 0420297, 10.4064/sm-55-1-27-40 |
| Reference:
|
[2] Bennett, G., Goodman, V., Newman, C. M.: Norms of random matrices.Pacific J. Math. 59 (1975), 359-365. Zbl 0325.47018, MR 0393085, 10.2140/pjm.1975.59.359 |
| Reference:
|
[3] Bergh, J., Löfström, J.: Interpolation Spaces.Springer, Berlin (1976). |
| Reference:
|
[4] Carl, B.: Inequalities between absolutely $(p,q)$-summing norms.Studia Math. 69 (1980), 143-148. Zbl 0468.47012, MR 0604346, 10.4064/sm-69-2-143-148 |
| Reference:
|
[5] König, H.: Interpolation of operator ideals with an application to eigenvalue distribution problems.Math. Ann. 233 (1978), 35-48. MR 0482266, 10.1007/BF01351495 |
| Reference:
|
[6] König, H.: Eigenvalue Distribution of Compact Operators.Birkhäuser, Basel (1986). MR 0889455 |
| Reference:
|
[7] Peetre, J., Sparr, G.: Interpolation of normed abelian groups.Ann. Mat. Pura Appl. 92 (1972), 217-262. Zbl 0237.46039, MR 0322529, 10.1007/BF02417949 |
| Reference:
|
[8] Pietsch, A.: Weyl numbers and eigenvalues of operators in Banach spaces.Math. Ann. 247 (1980), 149-168. Zbl 0428.47027, MR 0568205, 10.1007/BF01364141 |
| Reference:
|
[9] Pietsch, A.: Operator Ideals.North-Holland, Amsterdam (1980). Zbl 0455.47032, MR 0582655 |
| Reference:
|
[10] Pietsch, A.: Eigenvalues and $s$-numbers.Cambridge Univ. Press (1987). Zbl 0615.47019, MR 0890520 |
| Reference:
|
[11] Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators.North-Holland, Amsterdam (1978). Zbl 0387.46033, MR 0503903 |
| . |
