Artículo
Near-infinity concentrated norms and the fixed point property for nonexpansive maps on closed, bounded, convex sets
Autor/es | Castillo Santos, Francisco Eduardo
Dowling, Patrick N. Fetter Nathansky, Helga Andrea Japón Pineda, María de los Ángeles Lennard, Christopher J. Sims, Brailey Turett, Barry |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2018-08-01 |
Fecha de depósito | 2018-11-14 |
Publicado en |
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Resumen | In this paper we define the concept of a near-infinity concentrated norm on a Banach space X with a boundedly complete Schauder basis. When k · k is such a norm, we prove that (X, k · k) has the fixed point property (FPP); ... In this paper we define the concept of a near-infinity concentrated norm on a Banach space X with a boundedly complete Schauder basis. When k · k is such a norm, we prove that (X, k · k) has the fixed point property (FPP); that is, every nonexpansive self-mapping defined on a closed, bounded, convex subset has a fixed point. In particular, P.K. Lin’s norm in l1 [P.K. Lin, There is an equivalent norm on l1 that has the fixed point property, Nonlinear Anal. 68 (8) (2008), 2303-2308] and the norm νp(·) (with p = (pn) and limn pn = 1) introduced in [P.N. Dowling, W.B. Johnson, C.J. Lennard and B. Turett, The optimality of James’s distortion theorems, Proc. Amer. Math. Soc. 124 (1) (1997), 167-174] are examples of near-infinity concentrated norms. When νp(·) is equivalent to the l1-norm, it was an open problem as to whether (l1, νp(·)) had the FPP. We prove that the norm νp(·) always generates a nonreflexive Banach space X = R ⊕p1(R ⊕p2(R ⊕p3. . . )) satisfying the FPP, regardless of whether νp(·) is equivalent to the l1-norm. We also obtain some stability results. |
Identificador del proyecto | 243722
613207 MTM2015-65242-C2-1-P FQM-127 |
Cita | Castillo Santos, F.E., Dowling, P.N., Fetter Nathansky, H.A., Japón Pineda, M.d.l.Á., Lennard, C.J., Sims, B. y Turett, B. (2018). Near-infinity concentrated norms and the fixed point property for nonexpansive maps on closed, bounded, convex sets. Journal of Functional Analysis, 275 (3), 559-576. |
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