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Palazuelos Cabezón, Carlos ; Peralta Pereira, Antonio Miguel ; Villanueva, Ignacio | Polish Acad Sciencies Inst Mathematics | 2009In recent papers, the Right mid the Strong* topologies have been. introduced and studied on general Banach spaces We characterize different types of continuity for multilinear operators (joint, uniform, etc) with respect to the above topologies [...]texto impreso
Villanueva, Ignacio ; Palazuelos Cabezón, Carlos ; Peralta Pereira, Antonio Miguel | Oxford University Press | 2008-09We show that for every orthogonally additive scalar n-homogeneous polynomial P on a C*-algebra A there exists phi in A* satisfying P(x) = phi(x(n)), for each element x in A. The vector-valued analogue follows as a corollary.texto impreso
Villanueva, Ignacio ; Peralta Pereira, Antonio Miguel ; Wright, J. D. Maitland ; Ylinen, Kari | Cambridge University Press | 2010-05We introduce the concept of quasi-completely continuous multilinear operators and use this concept to characterize, for a wide class of Banach spaces X1, …, Xk, the multilinear operators T : X1 × … × Xk ? X with an X-valued Aron–Berner extension.texto impreso
A Banach space X has the Dunford–Pettis property (DPP) if and only if whenever (xn) and (pn) are weakly null sequences in X and X*, respectively, we have pn(xn)? 0. Freedman introduced a stricly weaker version of the DPP called the alternative D[...]texto impreso
Peralta Pereira, Antonio Miguel ; Villanueva, Ignacio ; Wright, J. D. Maitland ; Ylinen, Kari | Elsevier | 2007-01-15Let X be a Banach space. Then there is a locally convex topology for X, the “Right topology,” such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the “Right” topol[...]texto impreso
Villanueva, Ignacio ; Peralta Pereira, Antonio Miguel ; Wright, J. D. Maitland ; Ylinen, Kari | Cambridge University Press | 2010The strong* topology s_(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, _(X), is a stronger locally convex to[...]
