| Title:
|
On total incomparability of mixed Tsirelson spaces (English) |
| Author:
|
Bernués, Julio |
| Author:
|
Pascual, Javier |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
841-859 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form $T[(\mathcal M_k,\theta _k)_{k =1}^{l}]$ with index $i(\mathcal M_k)$ finite are either $c_0$ or $\ell _p$ saturated for some $p$ and we characterize when any two spaces of such a form are totally incomparable in terms of the index $i(\mathcal M_k)$ and the parameter $\theta _k$. Also, we give sufficient conditions of total incomparability for a particular class of spaces of the form $T[(\mathcal A_k,\theta _k)_{k = 1}^\infty ]$ in terms of the asymptotic behaviour of the sequence $\Bigl \Vert \sum _{i=1}^n e_i\Bigr \Vert $ where $(e_i)$ is the canonical basis. (English) |
| Keyword:
|
mixed Tsirelson spaces |
| Keyword:
|
totally incomparable spaces |
| MSC:
|
46B03 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 1080.46507 |
| idMR:
|
MR2018834 |
| . |
| Date available:
|
2009-09-24T11:07:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127844 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
