On stability of nonlinear non-surjective epsilon-isometries of Banach spaces

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	On stability of nonlinear non-surjective epsilon-isometries of Banach spaces
	Cheng, Lixin ; Dong, Yunbai ; Zhang, Wen ; Zhang W(张文)
刊名	http://dx.doi.org/10.1016/j.jfa.2012.11.008
	2013-02-01
关键词	epsilon-Isometry Nonlinear operator Stability Banach space
英文摘要	Let X, Y be two Banach spaces, epsilon >= 0, and let f : X -> Y be an epsilon-isometry with f(0) = 0. In this paper, we show first that for every x* is an element of X, there exists phi is an element of Y with vertical bar vertical bar phi vertical bar vertical bar = vertical bar vertical bar xvertical bar vertical bar r such that vertical bar - <(x, x)>vertical bar <= 4 epsilon r, for all x is an element of X. Making use of it, we prove that if Y is reflexive and if F subset of Y [the annihilator of the subspace F subset of Y* consisting of all functionals bounded on (co) over bar (f (X), - f (X))] is alpha-complemented in Y, then there is a bounded linear operator T: Y -> X with vertical bar vertical bar T vertical bar vertical bar <= alpha such that vertical bar vertical bar T f(x) - x vertical bar vertical bar <= 4 epsilon, for all x is an element of X. If, in addition, Y is Gateaux smooth, strictly convex and admitting the Kadec-Klee property (in particular, locally uniformly convex), then we have the following sharp estimate vertical bar vertical bar T f(x) - x vertical bar vertical bar <= 2 epsilon, for all x is an element of X.(C) 2012 Elsevier Inc. All rights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66246]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Cheng, Lixin,Dong, Yunbai,Zhang, Wen,et al. On stability of nonlinear non-surjective epsilon-isometries of Banach spaces[J]. http://dx.doi.org/10.1016/j.jfa.2012.11.008,2013.
APA	Cheng, Lixin,Dong, Yunbai,Zhang, Wen,&张文.(2013).On stability of nonlinear non-surjective epsilon-isometries of Banach spaces.http://dx.doi.org/10.1016/j.jfa.2012.11.008.
MLA	Cheng, Lixin,et al."On stability of nonlinear non-surjective epsilon-isometries of Banach spaces".http://dx.doi.org/10.1016/j.jfa.2012.11.008 (2013).