Open Problems In The Geometry And Analysis Of Banach Spaces
by Vicente Montesinos /
2016 / English / PDF
2.3 MB Download
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.
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.
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.
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.