We draw a fundamental compendium of the most valuable results of the theory of summing
linear operators and detail those that are not shared by known multilinear and polynomial …

Abstract The Hardy–Littlewood inequalities on ℓ p spaces provide optimal exponents for
some classes of inequalities for bilinear forms on ℓ p spaces. In this paper we investigate in …

We show that given a positive integer m, a real number and the set of non-multiple-summing
m-linear forms on contains, except for the null vector, a closed subspace of maximal …

Abstract For K= RK= R or CC, the Hardy–Littlewood inequality for m-linear forms asserts that
for 4 ≤ 2m ≤ p ≤ ∞ 4≤ 2 m≤ p≤∞ there exists a constant C_ m, p^ K ≥ 1 C m, p K≥ 1 …

Operators T that belong to some summing operator ideal can be characterized by means of
the continuity of an associated tensor operator TT¯ that is defined between tensor products …

It is well known that not every summability property for multilinear operators leads to a
factorization theorem. In this paper we undertake a detailed study of factorization schemes …

Let E and F be complex Banach spaces, U be an open subset of E and 1≤ p≤∞. We
introduce and study the notion of a Cohen strongly p-summing holomorphic map** from U …

We introduce a notion of (p, q)-dominated multilinear operators which stems from the
geometrical approach provided by Σ-operators. We prove that (p, q)-dominated multilinear …

We introduce the concept of vector-valued holomorphic map**s on the complex unit disk
that factor through a Hilbert space and state the main properties of the space formed by such …