The optimality of James's distortion theorems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The optimality of James's distortion theorems

Authors:	P N Dowling W B Johnson C J Lennard B Turett

Institution:	Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056 ; Department of Mathematics, Texas A&M University, College Station, Texas 77843 ; Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 ; Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309

Abstract:	A renorming of $\ell _{1}$ , explored here in detail, shows that the copies of $\ell _{1}$ produced in the proof of the Kadec-Pelczynski theorem inside nonreflexive subspaces of $L_{1}0,1]$ cannot be produced inside general nonreflexive spaces that contain copies of $\ell _{1}$ . Put differently, James's distortion theorem producing one-plus-epsilon-isomorphic copies of $\ell _{1}$ inside any isomorphic copy of $\ell _{1}$ is, in a certain sense, optimal. A similar renorming of $c_{0}$ shows that James's distortion theorem for $c_{0}$ is likewise optimal.

Keywords:	$\ell _{1}$ $c_{0}$ renorming James's distortion theorem asymptotically isometric copies of $\ell _{1}$ fixed point property

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文