Atomic decompositions for tensor products and polynomial spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:347

Article

Carando, Daniel¹  Lassalle, Silvia¹ 

[1] Univ Buenos Aires, Fac Cs Exactas & Nat, Dept Matemat Pab 1, RA-1428 Buenos Aires, DF, Argentina

关键词: atomic decompositions;    tensor products;    symmetric tensor norms;    homogeneous polynomials;    polynomial ideals;   

DOI  :  10.1016/j.jmaa.2008.05.051

来源: Elsevier

【 摘 要 】

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product circle times(n)(s,mu) X, for any symmetric tensor norm mu. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free