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Pellegrino, Daniel and SeoaneSepúlveda, Juan B. (2015) Grothendieck's theorem for absolutely summing multilinear operators is optimal. Linear & Multilinear Algebra, 63 (3). pp. 554558. ISSN 03081087

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/03081087.2013.877013#.VTDkqvmsWCl
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http://arxiv.org/pdf/1307.4809v2.pdf  Organisation 
Abstract
Grothendieck's theorem asserts that every continuous linear operator from ℓ1 to ℓ2 is absolutely (1;1)summing. In this note we prove that the optimal constant gm so that every continuous mlinear operator from ℓ1×⋯×ℓ1 to ℓ2 is absolutely (gm;1)summing is 2m+1. We also show that if gm<2m+1 there is c dimensional linear space composed by continuous non absolutely (gm;1)summing mlinear operators from ℓ1×⋯×ℓ1 to ℓ2. In particular, our result solves (in the positive) a conjecture posed by A.T. Bernardino in 2011.
Item Type:  Article 

Uncontrolled Keywords:  lineability, spaceability, absolutely summing operators 
Subjects:  Sciences > Mathematics 
ID Code:  29656 
Deposited On:  17 Apr 2015 11:23 
Last Modified:  25 Nov 2016 12:38 
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