Loading [MathJax]/extensions/MathZoom.js
We study the problem of whether , the space of n-homogeneous polynomials which are weakly continuous on bounded sets, is an M-ideal in the space (ⁿE) of continuous n-homogeneous polynomials. We obtain conditions that ensure this fact and present some examples. We prove that if is an M-ideal in (ⁿE), then coincides with (n-homogeneous polynomials that are weakly continuous on bounded sets at 0). We introduce a polynomial version of property (M) and derive that if and (E) is an M-ideal in...
We establish Hölder-type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain estimates for their norms. We also consider norms of multilinear forms in different Banach multilinear ideals.
Given Banach spaces , and a compact Hausdorff space , we use polymeasures to give necessary conditions for a multilinear operator from into to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for to have the Schur property (resp. to contain no copy of ), and for to be scattered. This extends results concerning linear operators.
Currently displaying 1 –
3 of
3