Download PDF - Spaces of Lipschitz functions on metric spacesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Spaces of Lipschitz functions on metric spaces

Authors 1, 2

Affiliations

  1. Institute of Operations Research, University of Karlsruhe - KIT, D-76128 Karlsruhe, Germany
  2. Faculty of Mathematics and Computer Science, FernUniversitaet Hagen, D-58084 Hagen, Germany

Abstract

In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.

Keywords

ENG
categories of Lipschitz spaces, Saks spaces, base normed spaces

Bibliography

  1. R.F. Arens and J. Eells, Jr, On embedding uniform and topological spaces, Pacific J. Math. 6 (1956), 397-403. doi: 10.2140/pjm.1956.6.397
  2. H. Bauer, Wahrscheinlichkeitstheorie (5te Auflage), de Gruyter Lehrbuch, Walter de Gruyter & Co. (Berlin, 2002).
  3. N. Bourbaki, Éléments de mathématique. XI. Première partie: Les structures fondamentales de l' analyse, no. 1102. Hermann et Cie. (Paris, 1950).
  4. N. Dunford and J.T. Schwartz, Linear Operators: Part I, Interscience Publishers, Inc. (New York, 1957).
  5. D. Pumplün, Elemente der Kategorientheorie, Hochschultaschenbuch (Spektrum Akademischer Verlag, Heidelberg, Berlin, 1999).
  6. D. Pumplün, The metric completion of convex sets and modules, Result. Math. 41 (2002), 346-360. doi: 10.1007/BF03322777
  7. D. Pumplün, A universal compactification of topological positively convex sets, J. Convex Anal. 18 (4) (2011), 999-1012.
  8. S. Rolewicz, Metric Linear Spaces, PWN - Polish Scientific Publishers, Warszawa and D. Reidel Publishing Company (Dordrecht, 1972).
  9. Z. Semadeni, Banach Spaces of Continuous Functions, Vol. I PWN - Polish Scientific Publishers (Warszawa, 1971).
  10. Z. Semadeni, Some Saks-space dualities in harmonic analysis on commutative semigroups, Special topics of applied mathematics (Proc. Sem., Ges. Math. Datenverarb., Bonn, 1979), 71-87 (North-Holland, Amsterdam-New York, 1980).
  11. D.R. Sherbert, The structure of ideals and point derivations in Banach Algebras of Lipschitz functions, Trans AMS 111 (1964), 240-272. doi: 10.1090/S0002-9947-1964-0161177-1
  12. Nik Weaver, Lipschitz Algebras, World Scientific (Singapore, New Jersey, London, Hong Kong, 1999).
  13. Yau Chuen Wong and Kung Fu Ng, Partially Ordered Topological Vector Spaces, Oxford Mathematical Monographs. Clarendon Press, Oxford, 1973.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2015/35/1
Export to PBN, Opens in new tab
Pages:
5-23
Main language of publication
English
Received
2015-05-31
Published
2015

DOI: 10.7151/dmdico.1170

Exact and natural sciences