The structure of ideals in the Banach algebra of Lipschitz functions over valued fields

R. Bhaskaran

Compositio Mathematica (1983)

  • Volume: 48, Issue: 1, page 25-34
  • ISSN: 0010-437X

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Bhaskaran, R.. "The structure of ideals in the Banach algebra of Lipschitz functions over valued fields." Compositio Mathematica 48.1 (1983): 25-34. <http://eudml.org/doc/89585>.

@article{Bhaskaran1983,
author = {Bhaskaran, R.},
journal = {Compositio Mathematica},
keywords = {complete ultrametric space; complete non-archimedean valued field; Lipschitz extension property; spherically complete; strongly semi-simple Banach algebra; Silov ideals; Gelfand transforms; Banach algebra of Lipschitz functions},
language = {eng},
number = {1},
pages = {25-34},
publisher = {Martinus Nijhoff Publishers},
title = {The structure of ideals in the Banach algebra of Lipschitz functions over valued fields},
url = {http://eudml.org/doc/89585},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Bhaskaran, R.
TI - The structure of ideals in the Banach algebra of Lipschitz functions over valued fields
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 1
SP - 25
EP - 34
LA - eng
KW - complete ultrametric space; complete non-archimedean valued field; Lipschitz extension property; spherically complete; strongly semi-simple Banach algebra; Silov ideals; Gelfand transforms; Banach algebra of Lipschitz functions
UR - http://eudml.org/doc/89585
ER -

References

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  1. [1] G. Bachman, E. Beckenstein, L. Narici and Seth Warner, Rings of continuous functions with values in a topological field, Trans. Amer. Math. Soc.204 (1975), 91-112. Zbl0299.54016MR402687
  2. [2] E. Beckenstein, G. Bachman and L. Narici, Topological algebras of continuous functions over valued fields, Studia Math.XLVIII (1973), 119-127. Zbl0281.46048MR331064
  3. [3] E. Beckenstein, G. Bachman and L. Narici, Function algebras over valued fields with measures IV, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat.53 (5) (1972), 349-358. Zbl0277.46023MR358324
  4. [4] R. Bhaskaran and U. Naik-Nimbalkar, Banach algebras of Lipschitz functions over valued fields, Indag. Math.40 (1978), 15-26. Zbl0402.46047MR482228
  5. [5] L. Gruson and M. Van Der Put, Banach spaces, Bull. Soc. Math. France, Memoire 39-40 (1974), 55-100. Zbl0312.46029MR365173
  6. [6] A.W. Ingleton, The Hahn-Banach theorem for non-archimedean valued fields, Proc. Cambridge Phil. Soc.48 (1952), 41-45. Zbl0046.12001MR45939
  7. [7] T.M. Jenkins, Banach spaces of Lipschitz functions on an abstract metric space, Thesis, Yale University, 1967. 
  8. [8] L.H. Loomis, An Introduction to Abstract Harmonic Analysis, van Nostrand, 1953. Zbl0052.11701MR54173
  9. [9] A.F. Monna, Analyse non-archimedienne, Springer-Verlag, 1970. Zbl0203.11501MR295033
  10. [10] L. Narici, E. Beckenstein and G. Bachman, Functional Analysis and Valuation Theory, Marcel Dekker, 1971. Zbl0218.46004MR361697
  11. [11] W.H. Schikhof, Non-archimedean Harmonic analysis, Thesis, Nijmegen, 1967. Zbl0154.15401
  12. [12] D.R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc.111 (1964), 240-272. Zbl0121.10204MR161177
  13. [13] G. Silov, Homogeneous rings of functions, Amer. Math. Soc. Transl.No. 92, 1953, Reprint Amer. Math. Soc. Transl. (1) (1962), 392-455. Zbl0053.08401MR56204
  14. [14] G.F. Simmons, Introduction to topology and modern Analysis, McGraw Hill, 1963. Zbl0105.30603MR146625
  15. [15] A.C.M. Van Rooij, Non-archimedean Functional Analysis, Lecture Notes, Catholic University, Nijmegen, 1976. 
  16. [16] A.C.M. Van Rooij, Non-archimedean Functional Analysis, Marcel Dekker, 1978. Zbl0396.46061MR512894
  17. [17] L. Waelbroeck, Closed ideals of Lipschitz functions, Proceedings of the International Symposium on Function algebras, Tulane University, 1965, 322-325. Zbl0145.16802MR194926

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