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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.
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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