Open Problems in the Geometry and Analysis of Banach Spaces

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Open Problems in the Geometry and Analysis of Banach Spaces by Antonio J. Guirao, Vicente Montesinos, Václav Zizler, Springer International Publishing
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Author: Antonio J. Guirao, Vicente Montesinos, Václav Zizler ISBN: 9783319335728
Publisher: Springer International Publishing Publication: July 26, 2016
Imprint: Springer Language: English
Author: Antonio J. Guirao, Vicente Montesinos, Václav Zizler
ISBN: 9783319335728
Publisher: Springer International Publishing
Publication: July 26, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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