Weak Grothendieck's theorem

Lahcène Mezrag

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-12

Abstract:

Let E n ⊂ L 1 2 n be the n -dimensional subspace which appeared in Kašin's theorem such that L 1 2 n = E n ⊕ E n ⊥ and the L 1 2 n and L 2 2 n norms are universally equivalent on both E n and E n ⊥ . In this paper, we introduce and study someproperties concerning extension and weak Grothendieck's theorem(WGT). We show that the Schatten space S p for all 0 < p ≤ ∞ does not verify the theorem of extension. We provealso that S p 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 forspaces verifying WGT.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:043875

DOI: 10.1155/IJMMS/2006/43875

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