Four Non-linear Problems on Normed Spaces: Volume I: 1 - Softcover

Garcia Pacheco, Francisco

Softcover

ISBN 10: 3639101820 ISBN 13: 9783639101829

Publisher: VDM Verlag Dr. Müller, 2008

Synopsis

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 García-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.

About this title

About the Author

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.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2008
• Language: English
• ISBN 10: 3639101820
• ISBN 13: 9783639101829
• Binding: Paperback
• Number of pages: 112