Isometries between spaces of homogeneous polynomials

BOYD, C., LASSALLE, S.

JOURNAL OF FUNCTIONAL ANALYSIS

Elsevier

Año: 2005 vol. 224 p. 281 - 295

0022-1236

We derive Banach–Stone theorems for spaces of homogeneous polynomials. We show that every isometric isomorphism between the spaces of homogeneous approximable polynomials on real Banach spaces E and F is induced by an isometric isomorphism of E' onto F'. With an additional geometric condition we obtain the analogous result in the complex case. Isometries between spaces of homogeneous integral polynomials and between the spaces of all n-homogeneous polynomials are also investigated.