Spectrum preserving linear mappings in Banach algebras

• Autorzy: B. Aupetit , H. du T. Mouton
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46Hxx: Topological algebras, normed rings and algebras, Banach algebras
• 17C65: Jordan structures on Banach spaces and algebras
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 1
• Strony: 91-100

Daty

wydano

1994

otrzymano

1993-06-24

poprawiono

1993-09-20

Twórcy

autor

B. Aupetit

• Département de Mathématiques et de Statistique, Université Laval, Québec, Canada, G1K 7P4

autor

H. du T. Mouton

• Department of Mathematics, University of the Orange Free State, Bloemfontein, 9300 South Africa

Bibliografia

• [1] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Berlin, 1979.
• [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.
• [4] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261.
• [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.
• [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.