Weak Grothendieck's theorem
Let En⊂L12n be the n-dimensional subspace which appeared in Kašin's theorem such that L12n=En⊕En⊥ and the L12n and L22n norms are universally equivalent on both En and En⊥. In this paper, we introduce and study some properties concerning extension and weak Grothendieck's theorem (WGT). We...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/43875 |
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| _version_ | 1832558833083351040 |
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| author | Lahcène Mezrag |
| author_facet | Lahcène Mezrag |
| author_sort | Lahcène Mezrag |
| collection | DOAJ |
| description | Let En⊂L12n be the n-dimensional subspace which appeared in Kašin's theorem such that L12n=En⊕En⊥ and the L12n and
L22n norms are universally equivalent on both En and En⊥. In this paper, we introduce and study some
properties concerning extension and weak Grothendieck's theorem
(WGT). We show that the Schatten space Sp for all 0<p≤∞ does not verify the theorem of extension. We prove
also that Sp fails GT for all 1≤p≤∞ and consequently by one result of Maurey does not satisfy WGT for
1≤p≤2. We conclude by giving a characterization for
spaces verifying WGT. |
| format | Article |
| id | doaj-art-dfdba16b15144e648dc23d2724706cb1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dfdba16b15144e648dc23d2724706cb12025-02-03T01:31:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/4387543875Weak Grothendieck's theoremLahcène Mezrag0Department of Mathematics, M'sila University, P.O. Box 166, M'sila 28000, AlgeriaLet En⊂L12n be the n-dimensional subspace which appeared in Kašin's theorem such that L12n=En⊕En⊥ and the L12n and L22n norms are universally equivalent on both En and En⊥. In this paper, we introduce and study some properties concerning extension and weak Grothendieck's theorem (WGT). We show that the Schatten space Sp for all 0<p≤∞ does not verify the theorem of extension. We prove also that Sp fails GT for all 1≤p≤∞ and consequently by one result of Maurey does not satisfy WGT for 1≤p≤2. We conclude by giving a characterization for spaces verifying WGT.http://dx.doi.org/10.1155/IJMMS/2006/43875 |
| spellingShingle | Lahcène Mezrag Weak Grothendieck's theorem International Journal of Mathematics and Mathematical Sciences |
| title | Weak Grothendieck's theorem |
| title_full | Weak Grothendieck's theorem |
| title_fullStr | Weak Grothendieck's theorem |
| title_full_unstemmed | Weak Grothendieck's theorem |
| title_short | Weak Grothendieck's theorem |
| title_sort | weak grothendieck s theorem |
| url | http://dx.doi.org/10.1155/IJMMS/2006/43875 |
| work_keys_str_mv | AT lahcenemezrag weakgrothendieckstheorem |