1.

Record Nr.

UNINA9910254065603321

Autore

Guirao Antonio J

Titolo

Open Problems in the Geometry and Analysis of Banach Spaces / / by Antonio J. Guirao, Vicente Montesinos, Václav Zizler

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016

ISBN

3-319-33572-3

Edizione

[1st ed. 2016.]

Descrizione fisica

1 online resource (XII, 169 p. 1 illus.)

Disciplina

515.7

Soggetti

Functional analysis

Approximation theory

Measure theory

Convex geometry

Discrete geometry

Algebraic topology

Functional Analysis

Approximations and Expansions

Measure and Integration

Convex and Discrete Geometry

Algebraic Topology

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and indexes.

Nota di contenuto

Preface -- Basic linear structure -- Basic linear geometry -- Biorthogonal systems -- Smoothness, smooth approximation -- Nonlinear geometry -- Some more nonseparable problems -- Some applications -- Bibliography -- List of concepts and problems -- Symbol index -- Subject index. .

Sommario/riassunto

This is a 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 convince 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 presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would require new ideas, while others 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.