Advertisement

Open Problems in the Geometry and Analysis of Banach Spaces

  • Antonio J. Guirao
  • Vicente Montesinos
  • Václav Zizler

Table of contents

  1. Front Matter
    Pages i-xii
  2. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 1-35
  3. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 37-50
  4. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 51-57
  5. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 59-102
  6. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 103-123
  7. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 125-128
  8. Antonio J. Guirao, Vicente Montesinos, Václav Zizler
    Pages 129-134
  9. Back Matter
    Pages 135-169

About this book

Introduction

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.

Keywords

topology nonlinear geometry fixed points convexity Banach spaces Schauder bases and biorthogonal systems approximation optimization differentiability renormings weak compact generating

Authors and affiliations

  • Antonio J. Guirao
    • 1
  • Vicente Montesinos
    • 2
  • Václav Zizler
    • 3
  1. 1.Departamento de Matemática AplicadaInstituto de Matemática Pura y Aplicada, Universitat Politècnica de ValènciaValenciaSpain
  2. 2.Departamento de Matemática AplicadaInstituto de Matemática Pura y Aplicada, Universitat Politècnica de ValènciaValenciaSpain
  3. 3.Department of Mathematical & Statistical SciencesUniversity of AlbertaEdmontonCanada

Bibliographic information