Complemented subspaces and interpolation properties in spaces of polynomials

[摘要] Let X be a Banach space whose dual X* has type p is an element of (1, 2]. If m is an integer greater than p/(p - 1) and (x(n)) is a seminormalized sequence weakly convergent to zero, there is a subsequence (y(n)) of (x(n)) such that, for each element (a(n)) of l(infinity), there is an m-homogeneous continuous polynomial P on X with P(y(n)) = a(n), n = 1, 2, ... . Some interpolation and complementation properties are also given in P((m)l(p)), for m < p, as well as in other spaces of polynomials and multilinear functionals. (C) 1997 Academic Press.

[发布日期] 1997-04-01