Hahn—Banach and Banach Open Mapping Theorems

  • 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

A real-valued function p on a vector space X is called a positively homogeneous sublinear functional if for all x, y ϵ X and α ≥ 0 it satisfies
$$p(\alpha x) = \alpha p(x)\;\;and\;\;p(x + y) \leqslant p(x) + p(y)$$
.

Keywords

Banach Space Normed Space Open Mapping Bounded Linear Operator Closed Subspace 
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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