Spaces of Lipschitz functions on metric spaces

Diethard Pallaschke; Dieter Pumplün

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2015)

  • Volume: 35, Issue: 1, page 5-23
  • ISSN: 1509-9407

Abstract

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

How to cite

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Diethard Pallaschke, and Dieter Pumplün. "Spaces of Lipschitz functions on metric spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 35.1 (2015): 5-23. <http://eudml.org/doc/276678>.

@article{DiethardPallaschke2015,
abstract = {In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.},
author = {Diethard Pallaschke, Dieter Pumplün},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {categories of Lipschitz spaces; Saks spaces; base normed spaces},
language = {eng},
number = {1},
pages = {5-23},
title = {Spaces of Lipschitz functions on metric spaces},
url = {http://eudml.org/doc/276678},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Diethard Pallaschke
AU - Dieter Pumplün
TI - Spaces of Lipschitz functions on metric spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2015
VL - 35
IS - 1
SP - 5
EP - 23
AB - In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
LA - eng
KW - categories of Lipschitz spaces; Saks spaces; base normed spaces
UR - http://eudml.org/doc/276678
ER -

References

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  2. [2] H. Bauer, Wahrscheinlichkeitstheorie (5te Auflage), de Gruyter Lehrbuch, Walter de Gruyter & Co. (Berlin, 2002). 
  3. [3] N. Bourbaki, Éléments de mathématique. XI. Première partie: Les structures fondamentales de l' analyse, no. 1102. Hermann et Cie. (Paris, 1950). 
  4. [4] N. Dunford and J.T. Schwartz, Linear Operators: Part I, Interscience Publishers, Inc. (New York, 1957). Zbl0128.34803
  5. [5] D. Pumplün, Elemente der Kategorientheorie, Hochschultaschenbuch (Spektrum Akademischer Verlag, Heidelberg, Berlin, 1999). 
  6. [6] D. Pumplün, The metric completion of convex sets and modules, Result. Math. 41 (2002), 346-360. doi: 10.1007/BF03322777 Zbl1034.52004
  7. [7] D. Pumplün, A universal compactification of topological positively convex sets, J. Convex Anal. 18 (4) (2011), 999-1012. Zbl1244.52004
  8. [8] S. Rolewicz, Metric Linear Spaces, PWN - Polish Scientific Publishers, Warszawa and D. Reidel Publishing Company (Dordrecht, 1972). 
  9. [9] Z. Semadeni, Banach Spaces of Continuous Functions, Vol. I PWN - Polish Scientific Publishers (Warszawa, 1971). 
  10. [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. [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 Zbl0121.10204
  12. [12] Nik Weaver, Lipschitz Algebras, World Scientific (Singapore, New Jersey, London, Hong Kong, 1999). 
  13. [13] Yau Chuen Wong and Kung Fu Ng, Partially Ordered Topological Vector Spaces, Oxford Mathematical Monographs. Clarendon Press, Oxford, 1973. Zbl0269.46007

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