Spectrum preserving linear mappings in Banach algebras

B. Aupetit; H. du T. Mouton

Studia Mathematica (1994)

  • Volume: 109, Issue: 1, page 91-100
  • ISSN: 0039-3223

Abstract

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Let A and B be two unitary Banach algebras. We study linear mappings from A into B which preserve the polynomially convex hull of the spectrum. In particular, we give conditions under which such surjective linear mappings are Jordan morphisms.

How to cite

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Aupetit, B., and du T. Mouton, H.. "Spectrum preserving linear mappings in Banach algebras." Studia Mathematica 109.1 (1994): 91-100. <http://eudml.org/doc/216063>.

@article{Aupetit1994,
abstract = {Let A and B be two unitary Banach algebras. We study linear mappings from A into B which preserve the polynomially convex hull of the spectrum. In particular, we give conditions under which such surjective linear mappings are Jordan morphisms.},
author = {Aupetit, B., du T. Mouton, H.},
journal = {Studia Mathematica},
keywords = {polynomially convex hull of the spectrum; surjective linear mappings; Jordan morphisms},
language = {eng},
number = {1},
pages = {91-100},
title = {Spectrum preserving linear mappings in Banach algebras},
url = {http://eudml.org/doc/216063},
volume = {109},
year = {1994},
}

TY - JOUR
AU - Aupetit, B.
AU - du T. Mouton, H.
TI - Spectrum preserving linear mappings in Banach algebras
JO - Studia Mathematica
PY - 1994
VL - 109
IS - 1
SP - 91
EP - 100
AB - Let A and B be two unitary Banach algebras. We study linear mappings from A into B which preserve the polynomially convex hull of the spectrum. In particular, we give conditions under which such surjective linear mappings are Jordan morphisms.
LA - eng
KW - polynomially convex hull of the spectrum; surjective linear mappings; Jordan morphisms
UR - http://eudml.org/doc/216063
ER -

References

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  1. [1] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Berlin, 1979. Zbl0409.46054
  2. [2] B. Aupetit, A Primer on Spectral Theory, Springer, Berlin, 1991. 
  3. [3] I. N. Herstein, Topics in Ring Theory, University of Chicago Press, Chicago, 1969. Zbl0232.16001
  4. [4] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
  5. [5] I. Kaplansky, Algebraic and Analytic Aspects of Operator Algebras, CBMS Regional Conf. Ser. in Math. 1, Amer. Math. Soc., Providence, 1970. 
  6. [6] 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
  7. [7] T. Mouton (H. du) and H. Raubenheimer, On rank one and finite elements of Banach algebras, Studia Math. 104 (1993), 211-219. 
  8. [8] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, 1960. 

Citations in EuDML Documents

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  1. Bojan Kuzma, Noninvertibility preservers on Banach algebras
  2. Takeshi Miura, Dai Honma, A generalization of peripherally-multiplicative surjections between standard operator algebras
  3. Abdelaziz Maouche, Formes multiplicatives à valeurs dans le spectre
  4. Robin Harte, On rank one elements
  5. Bernard Aupetit, Recent trends in the field of Jordan-Banach algebras
  6. Matej Brešar, Peter Šemrl, Finite rank elements in semisimple Banach algebras
  7. Bernard Aupetit, H. Mouton, Trace and determinant in Banach algebras
  8. Matej Brešar, Peter Šemrl, Linear preservers on ℬ(X)
  9. Youness Hadder, The kh-socle of a commutative semisimple Banach algebra

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