On automatic surjectivity of some additive transformations
DOI:
https://doi.org/10.4067/S0716-09172004000200004Keywords:
Banach spaces, additive transformations, quasi-nilpotent operators, automorphisms, antiautomorphism, espacios de Banach, operadores cuasi nilpotentes, automorfismos, antiautomorfismos, transformaciones aditivas.Abstract
Let X be an infinite dimensional Banach space and let ? : B(X) ? B(X) be a spectrum preserving additive transformation. We show that if the image of quasi-nilpotent operators contains all quasi-nilpotent operators, then ? is an automophism or an antiautomorphism of B(X).References
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[2] B. Aupetit and H. du Toit Mouton, Trace and determinant in Banach algebras, Studia. Math 121, pp. 115-136, (1996).
[3] B. Aupetit, Sur les transformations qui conservent le spectre, Banach. Algebras 97 (De Gryter, Berlin, pp. 55-78, (1998).
[4] B. Aupetit, A Primer On Spectral Theory (Springer New-York, (1991).
[5] M. Bresar and P. Semrl, Linear maps preserving the spectral radius, J. Funct. Anal 142, pp. 360-168, (1996).
[6] Fillmore, Sums of operators with square-zero, Acta. Sci. Math. Szeged. 28, pp. 285-288, (1967).
[7] A. A. Jafarian and A.R. Sourour, Spectrum preserving linear maps, J. Funct. Anal 66, pp. 255-261, (1986).
[8] M. Omladic and P. Semrl, Spectrum preserving additive maps, Linear. Algebras. Appl 153, pp. 67-72, (1991).
[9] W. Rudin, Functional Analysis.
[10] P. Semrl , Spectrally bounded linear maps on B(H), Quat. J. Math. Oxford (2) 49, pp. 87-92, (1998).
[11] P. Semrl, Linear maps that preserve the nilpotent operators, Acta. Sci. Math (szeged) 61, pp. 523-534, (1995).
[12] S. Sakai, C?-Algebras and W ?-Algebras (Springer,New-York, (1971).
[13] A.R. Sourour , Invertibility preserving linear maps on L(X), Trans. Amer. Soc 348, pp. 13-30, (1996).
Published
2017-05-22
How to Cite
[1]
M. Ech-chérif El Kettani and E. H. El Bouchibti, “On automatic surjectivity of some additive transformations”, Proyecciones (Antofagasta, On line), vol. 23, no. 2, pp. 111-121, May 2017.
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