Geraldo Botelho

Inclusions and coincidences for multiple summing multilinear mappings

Using complex interpolation we prove new inclusion and coincidence theorems for multiple (fully) summing multilinear and holomorphic mappings. Among several other results we show that continuous n- linear forms on cotype 2 spaces are multiple (2; q(k),..., q(k))-summing, where 2(k-1) = 0.

Two new properties of ideals of polynomials and applications

Abstract In this paper we introduce two properties for ideals of polynomials between Banach spaces and showhow useful they are to deal with several a priori different problems. By investigating these properties we obtain, among other results, new polynomial characterizations of L∞ spaces and characterizations of Banach spaces whose duals are isomorphic to f 1 (Λ).

Almost Summing Polynomials

This paper introduces the class of almost summing homogeneous polynomials between Banach spaces. A characterization by means of vector-valued sequences is proved, connections with the theory of absolutely summing polynomials are established and several examples are given. Some composition and coincidence theorems are obtained and the case of spaces with type or cotype is also investigated.

Scalar-valued dominated polynomials on Banach spaces

It is well known that 2-homogeneous polynomials on L ∞ -spaces are 2-dominated. Motivated by the fact that related coincidence results are possible only for polynomials defined on symmetrically regular spaces, we investigate the situation in several classes of symmetrically regular-spaces. We prove a number of non-coincidence results which makes us suspect that there is no infinite dimensional Banach space E such that every scalar-valued homogeneous polynomial on E is r-dominated for every r > 1.

Dominated polynomials on infinite dimensional spaces

The aim of this paper is to prove a stronger version of a conjecture posed earlier on the existence of nondominated scalar-valued m-homogeneous polynomials, m > 3, on arbitrary infinite dimensional Banach spaces.

Lineability of summing sets of homogeneous polynomials

Given a continuous n-homogeneous polynomial P : E ⟹ F between Banach spaces and 1 ≤ q ≤ p < ∞, in this article we investigate some properties concerning lineability and spaceability of the (p; q)-summing set of P, defined by S p; q (P) = {a ∈ E : P is (p; q)-summing at a}.

On Pietsch measures for summing operators and dominated polynomials

Let be the canonical map, where is a regular Borel probability measure on the closed unit ball of the dual of a Banach space endowed with the weak* topology. This paper has a twofold purpose: (i) to study when -summing linear operators/-dominated homogeneous polynomials on have a Pietsch measure for which the canonical map is injective; (ii) to show how these results can be used to correct the proofs of some results of the authors concerning Pietsch-type factorization of dominated polynomials.

On the transformation of vector-valued sequences by linear and multilinear operators

In this paper we provide a unifying approach to the study of Banach ideals of linear and multilinear operators defined, or characterized, by the transformation of vector-valued sequences. We also investigate the linear and multilinear stabilities of some frequently used classes of vector-valued sequences. Concrete applications are provided.

Dominated Bilinear Forms and 2-homogeneous Polynomials

The main goal of this note is to establish a connection between the cotype of the Banach space X and the parameters r for which every 2-homogeneous polynomial on X is r-dominated. Let cotX be the infimum of the cotypes assumed by X and (cotX)* be its conjugate. The main result of this note asserts that if cotX > 2, then for every 1<= r < (cotX)* there exists a non-r-dominated 2-homogeneous polynomial on X.

Summability and estimates for polynomials and multilinear mappings

Abstract In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on l p spaces in fact hold true for mappings on arbitrary Banach spaces.