Title: Four Non-linear Problems on Normed Spaces - Volume I (Paperback or Softback)
Publisher: VDM Verlag 12/29/2008
Publication Date: 2008
Language: English
ISBN 10: 3639101820
ISBN 13: 9783639101829
Binding: Paperback or Softback
Condition: New
Weight: 0.35 pounds
Book Type: Book

About this title

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 Garc�a-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 the Author

Francisco Garc�a 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 C�diz, EU. His dissertation (awarded as outstanding by Kent State Univ.) was on three of the four open problems covered in this book.

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