Displaying similar documents to “Absolutely- p -summing operators in r -spaces I”

The inclusion theorem for multiple summing operators

David Pérez-García (2004)

Studia Mathematica

Similarity:

We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.