Four Non-linear Problems on Normed Spaces - Volume I

ISBN-13: 9783639101829 / Angielski / Miękka / 2008 / 112 str.

Francisco Garcia Pacheco

Opis

This book deals with the following open problems: The Lineability Problem for Functionals (Aron and Gurariy, 2004); The Nowhere Density Problem for Functionals (Enflo, 2005); The Minimum-Norm Problem for Translations (Aizpuru and Garcia-Pacheco, 2003); The Banach-Mazur Conjecture for Rotations (Banach and Mazur, 1932). The first problem is on the linear structure of the set of norm-attaining functionals on a Banach space (it also considers the linear structure of the set of non-norm-attaining functionals). The second problem is on the topological structure of the set of norm-attaining functionals on a Banach space (it also considers the topological structure of the set of non-norm-attaining functionals). The third problem deals with the non-linear metric structure of translates of convex sets. Finally, the last problem deals with the isometric structure of the unit ball of a Banach space."

O autorze

Francisco García is a Visiting Assistant Professor in mathematics
at Texas A&M Univ. He has a doctorate in mathematics from Kent
State Univ., USA. He also has a doctorate in mathematics from the
University of Cádiz, EU. His dissertation (awarded as outstanding
by Kent State Univ.) was on three of the four open problems
covered in this book.