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Preservation of the Norms of Linear Operators Acting on Some Quaternionic Function Spaces

  • M. Elena Luna-Elizarrarás
  • Michael Shapiro
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 157)

Abstract

There are considered real and quaternionic versions of some classical linear spaces, such as Lebesgue spaces, the spaces of continuous functions, etc., as well as linear operators acting on them. We prove that, given a real linear bounded operator on one of those spaces its quaternionic extension keeps being bounded and its norm does not change.

Keywords

Quaternionic function spaces quaternionic linear operators norms of quaternionic extensions of linear operators 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • M. Elena Luna-Elizarrarás
    • 1
  • Michael Shapiro
    • 1
  1. 1.Departamento de MatemáticasE.S.F.M. del I.P.N.México, D.F.México

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