On Sharp Formulae for the Weak and the Strong Stability of ɛ-Isometries
Speaker:Prof. Lixin Cheng
School of Mathematical Sciences
Xiamen University
Date & Time:5 Feb 2013 (Tuesday) 10:30
Venue:J316
Organized by:Department of Mathematics

Abstract

The study of isometries between Banach spaces and its generalizations has continued for over 80 years since Mazur and Ulam 1932’s remarkable result: Every onto isometry between two Banach spaces is necessarily a_ne. A mapping f from a Banach space X to another Banach space Y is said to be an ɛ-isometry provided

for some constant If we call the mapping f an isometry. In this talk, first, we present a historical survey for the study of properties of such mappings. Then we talk about the broad background of ɛ-isometries in both pure and applied mathematics. Finally, we focus on the recent results concerning weak stability and strong stability and sharp formulae of non-surjective ɛ -isometries defined on wedges.
Biography

Prof. Lixin Cheng is currently a Professor in Xiamen University. Prof. Cheng obtained his Ph.D. degree in Harbin Institute of Technology. He is also the Editorial board member of various journals, such as, the Journal of Mathematical Research, the (Chinese) Adv. Math., and The Open Math Journal. Prof. Cheng is interested in Functional Analysis, Geometry of Infinite Dimensional Spaces, Convex Analysis. The publications of Prof. Cheng include, On Super Weakly Compact Convex Sets and Representation of the Dual of the Normed Semigroup They Generate, A sharp operator version of the Bishop-Phelps theorem for operators from  CL-spaces, On stability of nonlinear non-surjective ɛ-isometries of Banach spaces etc.