Extension of vector-valued integral polynomial

DANIEL CARANDO; SILVIA LASSALLE

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Elsevier Science (Academic Press)

Lugar: San Diego; Año: 2005 vol. 307 p. 77 - 85

0022-247X

We study the extendibility of integral vector-valued polynomialson Banach spaces. We prove that an $X$-valued Pietsch-integralpolynomial on $E$ extends to an $X$-valued Pietsch-integralpolynomial on any space $F$ containing $E$, with the same integralnorm. This is not the case for Grothendieck-integral polynomials:they do not always extend to $X$-valued Grothendieck-integralpolynomials. However, they are extendible to $X$-valuedpolynomials. The Aron-Berner extension of an integral polynomialis also studied. A canonical integral representation is given fordomains not containing $\ell_1$.