in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

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 spac...

We derive Banach-Stone theorems for spaces of homogeneous polynomials. We show that every isometric isomorphism between the spaces of n-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 n-homogeneous integ...

The notion of operators ideals goes back to Grothendieck [10] and its natural extension to polynomials and multilinear mappings is credited to Pietsch [24]. We prove some results on ideals of polynomials and obtain, as corollaries and particular cases, new properties concerning dominated, almost summing, integral polynomials and related ideals. Among other results, we obtain Extrapolation and D...