Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896618 | Journal of Functional Analysis | 2018 | 14 Pages |
Abstract
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 ââ
â is such a norm, we prove that (X,ââ
â) 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 â1[14] and the norm νp(â
) (with p=(pn) and limnâ¡pn=1) introduced in [3] are examples of near-infinity concentrated norms. When νp(â
) is equivalent to the â1-norm, it was an open problem as to whether (â1,νp(â
)) had the FPP. We prove that the norm νp(â
) always generates a nonreflexive Banach space X=Râp1(Râp2(Râp3â¦)) satisfying the FPP, regardless of whether νp(â
) is equivalent to the â1-norm. We also obtain some stability results.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
F.E. Castillo-Sántos, P.N. Dowling, H. Fetter, M. Japón, C.J. Lennard, B. Sims, B. Turett,