Renorming James Tree Space
نویسندگان
چکیده
We show that James tree space JT can be renormed to be Lipschitz separated. It negatively answers the question of J. Borwein, J. Giles and J. Vanderwerff whether every Lipschitz separated Banach space is an Asplund space.
منابع مشابه
Renormings of the Dual of James Tree Spaces
We discuss renorming properties of the dual of a James tree space JT . We present examples of weakly Lindelöf determined JT such that JT ∗ admits neither strictly convex nor Kadec renorming and of weakly compactly generated JT such that JT ∗ does not admit Kadec renorming although it is strictly convexifiable. The norm of a Banach space is said to be locally uniformly rotund (LUR) if for every ...
متن کاملOn non-midpoint locally uniformly rotund normability in Banach spaces
We will show that if X is a tree-complete subspace of ∞ , which contains c 0 , then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming. 1. Introduction. It is known that ∞ has an equivalent strictly convex renorming [2]; however, by a result due to Lindenstrauss, it cannot be equivalently renormed in locally u...
متن کاملUniformly smooth renorming of Banach spaces with modulus of convexity of power type 2
An upper bound q(c) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity satisfying δX(ε) cε2, is found. The estimate is asymptotically sharp and is expressed in terms of linear fractional function q(c). © 2006 Elsevier Inc. All rights reserved.
متن کاملA Characterization of Reflexivity
We give a characterization of reflexivity in terms of rotundity of the norm. Renorming characterization of various classes of Banach spaces is important and useful for applications. Some classes turn out to have very elegant descriptions, while most seem to resist the renorming point of view. The most spectacular result in this area is certainly the Enflo-Pisier characterization of superreflexi...
متن کاملMetrizability of Cone Metric Spaces Via Renorming the Banach Spaces
In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.
متن کامل