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Four Non-linear Problems on Normed Spaces - Volume I
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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.
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