Atomic decompositions for tensor products and polynomial spaces

CARANDO, D., LASSALLE S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Elsevier

Año: 2008 vol. 347 p. 243 - 254

0022-247X

We study the existenceof atomic decompositions for tensor products of Banach spaces andspaces of homogeneous polynomials. If a Banach space $X$ admits anatomic decomposition of a certain kind, we show that the symmetrizedtensor product of the elements of the atomic decomposition providesan atomic decomposition for the symmetric tensor product$ f{n}_{s,mu} X$, for any symmetric tensor norm $mu$. Inaddition, the reciprocal statement is investigated and analogousconsequences for the full tensor product are obtained. Finally we applythe previous results to establish the existence of monomial atomicdecompositions for certain ideals of polynomials on $X$.