# Spectrum preserving linear mappings in Banach algebras

Studia Mathematica (1994)

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

## Access Full Article

top## Abstract

top## How to cite

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

## Citations in EuDML Documents

top- Bojan Kuzma, Noninvertibility preservers on Banach algebras
- Takeshi Miura, Dai Honma, A generalization of peripherally-multiplicative surjections between standard operator algebras
- Abdelaziz Maouche, Formes multiplicatives à valeurs dans le spectre
- Robin Harte, On rank one elements
- Bernard Aupetit, Recent trends in the field of Jordan-Banach algebras
- Matej Brešar, Peter Šemrl, Finite rank elements in semisimple Banach algebras
- Bernard Aupetit, H. Mouton, Trace and determinant in Banach algebras
- Matej Brešar, Peter Šemrl, Linear preservers on ℬ(X)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.