Classical Banach Lattices

  • Peter Meyer-Nieberg
Part of the Universitext book series (UTX)


This section is concerned with C(K)-spaces and M-spaces. In particular, will we deduce those properties of C(K)-spaces which are closely related to the theory of Riesz spaces. An important result presented here is Kakutani’s representation theorem for an M-spaces with a unit. It plays still an important role in the theory of Riesz spaces, although many proofs which were originally based on this representation theorem now can be replaced by shorter and simpler lattice theoretical arguments.


Banach Lattice Riesz Space Banach Function Space Lattice Homomorphism Order Continuity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Peter Meyer-Nieberg
    • 1
  1. 1.Fachbereich MathematikUniversität OsnabrückOsnabrückFed.Rep.of Germany

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