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In this paper we prove a general version of the extrapolation theorem for absolutely summing nonlinear operators. It is explicitly shown that this result encompasses the previous old and recent, linear and nonlinear extrapolation theorems as par[...]texto impreso
Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier Science | 2012-01In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question a[...]texto impreso
Botelho, Geraldo ; Cariello, Daniel ; Favaro, Vinicius V. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Polish Acad Sciencies Inst Mathematics | 2013Let (Omega, Sigma, mu) be a measure space and 1texto impreso
In this note, we prove a general version of the Extrapolation Theorem for absolutely summing operators, extending the classical theorem due to B. Maurey ['Theoremes de factorisation pour les operateurs a valeurs dans les espaces L-p', Soc. Math.[...]texto impreso
Grothendieck's theorem asserts that every continuous linear operator from ?1 to ?2 is absolutely (1;1)-summing. In this note we prove that the optimal constant gm so that every continuous m-linear operator from ?1×?×?1 to ?2 is absolutely (gm;1)[...]texto impreso
Ciesielski, Krzysztof Chris ; Gámez Merino, José Luis ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier Science | 2014-01-01We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of [...]texto impreso
Bernal González, Luis ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2014For the last decade there has been a generalized trend in mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special prop[...]texto impreso
A classical inequality due to Bohnenblust and Hille states that for every positive integer m there is a constant C(m) > 0 so that (Sigma(N)(i1...., im=1) vertical bar U(e(i1), ..., e(im))vertical bar(2m/m+1))(m+1/2m) C, where C(m) = m(m+1/2m[...]texto impreso
Bernardino, Adriano Thiago ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. ; Souza, Marcela L.V. | Springer | 2015-06In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these generalizations [...]texto impreso
The search for sharp constants for inequalities of the type Littlewood's 4/3 and Bohnenblust-Hille has lately shown unexpected applications in many fields such as Analytic Number Theory, Quantum Information Theory, or in results on n-dimensional[...]texto impreso
Albuquerque, N. ; Bayart, F. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Springer Verlag | 2015In this paper we obtain quite general and definitive forms for Hardy–Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show [...]texto impreso
Botelho, G. ; Favaro, V.V. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier Science | 2012In this short note we prove the result stated in the title: that is, for every p > 0 there exists an infinite dimensional closed linear sub-space of L-p[0, 1] every nonzero element of which does not belong to boolean OR(q> p) L-q[0, 1]. This an[...]texto impreso
Albuquerque, N. ; Bayart, F. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier | 2014-03-15We prove that the multilinear Bohnenblust Hille inequality is a particular case of a quite general family of optimal inequalities.texto impreso
In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second result, mor[...]texto impreso
Diniz, D. ; Muñoz-Fernández, Gustavo A. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier | 2012The search of sharp estimates for the constants in the Bohnenblust-Hille inequality, besides its challenging nature, has quite important applications in different fields of mathematics and physics. For homogeneous polynomials, it was recently sh[...]
