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

top
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

top

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

top
  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

top
  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)

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.