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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |