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

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

How to cite

top

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

top
  1. [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 Zbl0073.39601
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.