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Proyecciones (Antofagasta)
versión impresa ISSN 0716-0917
Proyecciones (Antofagasta) v.23 n.2 Antofagasta ago. 2004
http://dx.doi.org/10.4067/S0716-09172004000200004
Proyecciones ON AUTOMATIC SURJECTIVITY OF SOME ADDITIVE TRANSFORMATIONS
MUSTPHA ECH-CHÉRIF EL KETTANI Universidad de Fes, Maroc Received : May 2003. Accepted : May 2004. Abstract Let X be an infinite dimensional Banach space and let Φ: 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 Φ is an automophism or an antiautomorphism of B(X). References [1] B. Aupetit, Une généralisation du théorème de Gleason-Kahane-Zelazko pour les algèbres de Banach, Pacific. J. Math 85, pp. 11-17, (1979). [ Links ] [2] B. Aupetit and H. du Toit Mouton, Trace and determinant in Banach algebras, Studia. Math 121, pp. 115-136, (1996). [ Links ] [3] B. Aupetit, Sur les transformations qui conservent le spectre, Banach. Algebras 97 (De Gryter, Berlin, pp. 55-78, (1998). [ Links ] [4] B. Aupetit, A Primer On Spectral Theory (Springer New-York, (1991). [ Links ] [5] M. Brear and P. emrl, Linear maps preserving the spectral radius, J. Funct. Anal 142, pp. 360-168, (1996). [ Links ] [6] Fillmore, Sums of operators with square-zero, Acta. Sci. Math. Szeged. 28, pp. 285-288, (1967). [ Links ] [7] A. A. Jafarian and A.R. Sourour, Spectrum preserving linear maps, J. Funct. Anal 66, pp. 255-261, (1986). [ Links ] [8] M.Omladic and P. emrl, Spectrum preserving additive maps, Linear. Algebras. Appl 153, pp. 67-72, (1991). [ Links ] [9] W. Rudin, Functional Analysis. [ Links ] [10] P. emrl , Spectrally bounded linear maps on B(H), Quat. J. Math. Oxford (2) 49, pp. 87-92, (1998). [ Links ] [11] P. emrl, Linear maps that preserve the nilpotent operators, Acta. Sci. Math (szeged) 61, pp. 523-534, (1995). [ Links ] [12] S. Sakai, C¤-Algebras and W¤-Algebras (Springer,New-York, (1971). [ Links ] [13] A.R. Sourour , Invertibility preserving linear maps on L(X), Trans. Amer. Soc 348, pp. 13-30, (1996). [ Links ]
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