The Gleason-Kahane-Żelazko theorem and its generalizations

A. Sourour

Banach Center Publications (1994)

  • Volume: 30, Issue: 1, page 327-331
  • ISSN: 0137-6934

Abstract

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This expository article deals with results surrounding the following question: Which pairs of Banach algebras A and B have the property that every unital invertibility preserving linear map from A to B is a Jordan homomorphism?

How to cite

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Sourour, A.. "The Gleason-Kahane-Żelazko theorem and its generalizations." Banach Center Publications 30.1 (1994): 327-331. <http://eudml.org/doc/262756>.

@article{Sourour1994,
abstract = {This expository article deals with results surrounding the following question: Which pairs of Banach algebras A and B have the property that every unital invertibility preserving linear map from A to B is a Jordan homomorphism?},
author = {Sourour, A.},
journal = {Banach Center Publications},
keywords = {Banach algebras; unital invertibility preserving linear map; Jordan homomorphism},
language = {eng},
number = {1},
pages = {327-331},
title = {The Gleason-Kahane-Żelazko theorem and its generalizations},
url = {http://eudml.org/doc/262756},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Sourour, A.
TI - The Gleason-Kahane-Żelazko theorem and its generalizations
JO - Banach Center Publications
PY - 1994
VL - 30
IS - 1
SP - 327
EP - 331
AB - This expository article deals with results surrounding the following question: Which pairs of Banach algebras A and B have the property that every unital invertibility preserving linear map from A to B is a Jordan homomorphism?
LA - eng
KW - Banach algebras; unital invertibility preserving linear map; Jordan homomorphism
UR - http://eudml.org/doc/262756
ER -

References

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  1. [1] B. Aupetit, Propriétés Spectrales des Algèbres des Banach, Lecture Notes in Math. 735, Springer, 1979. Zbl0409.46054
  2. [2] M.-D. Choi, D. Hadwin, E. Nordgren, H. Radjavi and P. Rosenthal, On positive linear maps preserving invertibility, J. Funct. Anal. 59 (1984), 462-469. Zbl0551.46040
  3. [3] J. Dieudonné, Sur une généralisation du groupe orthogonal à quatre variables, Arch. Math. (Basel) 1 (1949), 282-287. Zbl0032.10601
  4. [4] M. Eidelheit, On isomorphisms of rings of linear operators, Studia Math. 9 (1940), 97-105. Zbl0061.25301
  5. [5] A. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171-172. Zbl0148.37502
  6. [6] I. N. Herstein, Topics in Ring Theory, University of Chicago Press, Chicago, 1969. Zbl0232.16001
  7. [7] J.-C. Hou, Rank preserving linear maps on ℬ(X), Science in China (Series A) 32 (1989), 929-940. Zbl0686.47030
  8. [8] A. Jafarian and A. R. Sourour, Spectrum preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
  9. [9] J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343. Zbl0155.45803
  10. [10] I. Kaplansky, Algebraic and Analytic Aspects of Operator Algebras, Amer. Math. Soc., Providence, 1970. Zbl0217.44902
  11. [11] M. Marcus and R. Purves, Linear transformations on algebras of matrices: The invariance of the elementary symmetric functions, Canad. J. Math. 11 (1959), 383-396. Zbl0086.01704
  12. [12] M. Roitman and Y. Sternfeld, When is a linear functional multiplicative?, Trans. Amer. Math. Soc. 267 (1981), 111-124. Zbl0474.46039
  13. [13] B. Russo, Linear mappings of operator algebras, Proc. Amer. Math. Soc. 17 (1966), 1019-1022. Zbl0166.40003
  14. [14] A. R. Sourour, Invertibility preserving linear maps, preprint, 1992. 
  15. [15] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83-85. Zbl0162.18504

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