Locally uniformly rotund points in convex-transitive Banach spaces
نویسندگان
چکیده
منابع مشابه
On 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 کاملLocally Uniformly Convex Norms in Banach Spaces and Their Duals
It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.
متن کاملUniformly convex Banach spaces are reflexive - constructively
We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly convex Banach spaces are reflexive. Our aim in this note is to present a fully constructive analysis of the Milman-Pettis theorem [11, 12, 9, 13]: a uniformly convex Banach space is reflexive. First, t...
متن کاملUniformly Convex Functions on Banach Spaces
We study the connection between uniformly convex functions f : X → R bounded above by ‖ · ‖p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X → R bounded above by ‖ · ‖2 if and only if X admits an equivalent norm with modulus of convexity of power type 2.
متن کاملThe Geometry of Convex Transitive Banach Spaces
Throughout this paper, X will denote a Banach space, S ̄S(X ) and B ̄B(X ) will be the unit sphere and the closed unit ball of X, respectively, and ' ̄'(X ) will stand for the group of all surjective linear isometries on X. Unless explicitly stated otherwise, all Banach spaces will be assumed to be real. Nevertheless, by passing to real structures, the results remain true for complex spaces. Recal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.06.039