posted on 2025-05-11, 22:34authored byJonathan M. Borwein, A. J. Guirao, P. Hájek, J. Vanderwerff
Given a Banach space (Χ,∥ · ∥), we study the connection between
uniformly convex functions f : Χ → 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 : Χ → ℝ bounded above by ∥ · ∥² if and only if Χ admits an equivalent norm with modulus of convexity of power type 2.
History
Journal title
Proceedings of the American Mathematical Society
Volume
137
Issue
3
Pagination
1081-1091
Publisher
American Mathematical Society
Language
en, English
College/Research Centre
Faculty of Science and Information Technology
School
School of Mathematical and Physical Sciences
Rights statement
First published in the Proceedings of the American Mathematical Society in 2009, published by the American Mathematical Society.