K-bounded polynomials

CARANDO, D., DIMANT, V., DUARTE, B., LASSALLE S.

Math. Proc. R. Ir. Acad.

Año: 1998 vol. 98 p. 159 - 171

1393-7197

For a Banach space E we define the class  P_K (^N E) of K-bounded N-homogeneous polynomials, where K is a bounded subset of E'. We investigate properties of K which relate the space P_K (^N E) with usual subspaces of P(^N E). We prove that K-bounded polynomials are approximable when K is a compact set where the identity can be uniformly approximated by finite rank operators. The same is true when K is contained in the absolutely convex hull of a weakly nullbasic sequence of E'. Moreover, in this case we prove that every K-bounded polynomial is extendible to any larger space.