A Banach space in which all compact sets, but not all - download pdf or read online

By Vesely L.

Given a Banach spaceX, letc 0(X) be the distance of all null sequences inX (equipped with the supremum norm). We exhibit that: 1) every one compact set inc 0(X) admits a (Chebyshev) middle iff each one compact set inX admits a middle; 2) forX fulfilling a undeniable situation (Q), every one bounded set inc 0(X) admits a middle iffX is quasi uniformly rotund. We build a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the situation (Q) andX isn't really quasi uniformly rotund. It follows that the Banach spaceE=c 0(X) has the valuables from the name.

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Additional resources for A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers

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Trees from this genus typically have tall and straight single trunks, with bark that tends to remain thin and smooth until more advanced ages than in other tree species (Eckenwalder, 1996; Dickmann, 2001). They rarely live longer than 100–200 years, but are among the fastest growing temperate trees and can reach large sizes. A notable example is black cottonwood (Populus trichocarpa), which can exceed 60 m in height and reach up to 3 m in diameter (DeBell, 1990). Leaves are alternate and simple, with pinnato-palmate venation, and petioles are often transversally flattened distally (Eckenwalder, 1996).

2004) Characterization of microsatellites revealed by genomic sequencing of Populus trichocarpa. Can J For Res 34:85–93. Tuskan GA, DiFazio SP, Jansson S et al. (2006) The genome of black cottonwood, Populus trichocarpa (Torr. & Gray). Science 313:1596–1604. van Loo M, Joseph JA, Heinze B, Fay MF, Lexer C (2008) Clonality and spatial genetic structure in Populus x canescens and its sympatric backcross parent P. alba in a Central European hybrid zone. New Phytol 177:506–516. Vanden Broeck A, Cottrell J, Quataert P et al.

Assessed with isozymes and microsatellites. Mol Ecol 7:317–328. Suvanto LI, Latva-Karjanmaa TB (2005) Clone identification and clonal structure of the European aspen (Populus tremula). Mol Ecol 14:2851–2860. Tabbener HE, Cottrell JE (2003) The use of PCR based DNA markers to study the paternity of poplar seedlings. For Ecol Manag 179:363–376. Thevs N, Zerbe S, Schnittler M, Abdusalih N, Succow M (2008) Structure, reproduction and floodinduced dynamics of riparian Tugai forests at the Tarim River in Xinjiang, NW China.

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A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers by Vesely L.


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