Centralisers of spaces of symmetric tensor products and applications

BOYD, C., LASSALLE, S.

MATHEMATISCHE ZEITSCHRIFT

Springer-Verlag

Año: 2006 vol. 254 p. 539 - 552

0025-5874

We show that the centraliser of the space of n-fold symmetric injective tensors, n≥2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spaces. In addition, we derive a Banach-Stone Theorem for spaces of vector-valued approximable polynomials.