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Basic Concepts in Banach Spaces

  • Marián Fabian
  • Petr Habala
  • Petr Hájek
  • Vicente Montesinos Santalucía
  • Jan Pelant
  • Václav Zizler
Part of the Canadian Mathematical Society / Société mathématique du Canada book series (CMSBM)

Abstract

Most of the theory presented in this text is valid for both real and complex scalar fields. When the proofs are similar, we formulate the theorems without specifying the field over which we are working. When theorems are not valid in both fields or their proofs are different, we specify the scalar field in the formulation of a theorem. K denotes simultaneously the real (R) or complex (C) scalar field. We use N for {1,2,...}. All topologies are assumed to be Hausdorff. In particular, by a compact space we mean a compact Hausdorff space.

Keywords

Hilbert Space Banach Space Vector Space Basic Concept Orthonormal Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Marián Fabian
    • 1
  • Petr Habala
    • 2
  • Petr Hájek
    • 1
  • Vicente Montesinos Santalucía
    • 3
  • Jan Pelant
    • 1
  • Václav Zizler
    • 4
  1. 1.Mathematical InstituteCzech Academy of SciencesPrague 1Czech Republic
  2. 2.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical UniversityPrague 6Czech Republic
  3. 3.Department of Applied Mathematics, Telecommunication Engineering FacultyPolytechnic University of ValenciaValenciaSpain
  4. 4.Department of MathematicsUniversity of AlbertaEdmontonCanada

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