Bombal Gordón, Fernando and Fernández Unzueta, M. and Villanueva Díez, 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
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.
|Uncontrolled Keywords:||Polynomials; Tensor products; Complemented copies; Banach spaces|
|Subjects:||Sciences > Mathematics > Mathematical analysis|
|Deposited On:||24 Apr 2012 13:00|
|Last Modified:||14 Jan 2013 15:40|
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