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Local structure and copies of c(0) and l(1) in the tensor product of Banach spaces

Bombal Gordón, Fernando and Fernández Unzueta, M. and Villanueva, Ignacio (2004) Local structure and copies of c(0) and l(1) in the tensor product of Banach spaces. Boletín de la Sociedad Matemática Mexicana, 10 (2). pp. 195-202. ISSN 1405-213X

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Abstract

We use well known properties of the tensor product of l(p)-spaces to study the local structure of projective and injective tensor products of Banach spaces. In particular we give a simple proof of the fact that the injective (resp. projective) tensor product of infinite dimensional Banach spaces contains the l(infinity)(n)'s (resp., l(1)(n)'s) uniformly complemented. We then refine the previous arguments to give criteria for obtaining copies (complemented or not) of c(0) in the injective tensor product of Banach spaces, and complemented copies of l(1) in the projective tenser product of Banach spaces.


Item Type:Article
Uncontrolled Keywords:Polynomials; Tensor products; Complemented copies; Banach spaces
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:14947
Deposited On:24 Apr 2012 11:00
Last Modified:11 Dec 2013 18:14

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