Open Problems in the Geometry and Analysis of Banach Spaces

Front Cover
This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry.
The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study.

Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.
 

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Contents

1 Basic Linear Structure
1
2 Basic Linear Geometry
37
3 Biorthogonal Systems
51
4 Differentiability and Structure Renormings
58
5 Nonlinear Geometry
103
6 Some More Nonseparable Problems
125
7 Some Applications
129
References
135
List of Concepts and Problems
149
Symbol Index
157
Subject Index
159
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