# The Gleason-Kahane-Żelazko theorem and its generalizations

Banach Center Publications (1994)

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

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topSourour, 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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- [6] I. N. Herstein, Topics in Ring Theory, University of Chicago Press, Chicago, 1969. Zbl0232.16001
- [7] J.-C. Hou, Rank preserving linear maps on ℬ(X), Science in China (Series A) 32 (1989), 929-940. Zbl0686.47030
- [8] A. Jafarian and A. R. Sourour, Spectrum preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
- [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] I. Kaplansky, Algebraic and Analytic Aspects of Operator Algebras, Amer. Math. Soc., Providence, 1970. Zbl0217.44902
- [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] M. Roitman and Y. Sternfeld, When is a linear functional multiplicative?, Trans. Amer. Math. Soc. 267 (1981), 111-124. Zbl0474.46039
- [13] B. Russo, Linear mappings of operator algebras, Proc. Amer. Math. Soc. 17 (1966), 1019-1022. Zbl0166.40003
- [14] A. R. Sourour, Invertibility preserving linear maps, preprint, 1992.
- [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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