Abstract:
We introduce some new linear and multilinear ideals, and to study the
representation of these ideals by suitable tensor norms. We show that the results that
worked for the case of the multi-ideals involving summability could be extended to
the more general setting that is constructed starting from the interpolation method,
as inclusion theorems, Pietsch's domination theorem, factorization theorems and
characterizations by using the adjoints of m-linear operators. We also introduce
the ideal of ( p,σ ) -continuous polynomials that extends the nowadays well-known
ideal to the more general setting of the interpolated ideals of polynomials. We give a
factorization theorem for this new ideal which requires new techniques inspired in
the theory of Banach lattices.
