Spectrally Bounded Linear Maps on $B\text{(X)}$
Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 369-372

Voir la notice de l'article provenant de la source Cambridge University Press

We characterize surjective linear maps on $B\text{(X)}$ that are spectrally bounded and spectrally bounded below.
DOI : 10.4153/CMB-2004-036-4
Mots-clés : 47B49, spectrally bounded linear map
Fošner, Ajda; Šemrl, Peter. Spectrally Bounded Linear Maps on $B\text{(X)}$. Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 369-372. doi: 10.4153/CMB-2004-036-4
@article{10_4153_CMB_2004_036_4,
     author = {Fo\v{s}ner, Ajda and \v{S}emrl, Peter},
     title = {Spectrally {Bounded} {Linear} {Maps} on $B\text{(X)}$},
     journal = {Canadian mathematical bulletin},
     pages = {369--372},
     year = {2004},
     volume = {47},
     number = {3},
     doi = {10.4153/CMB-2004-036-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-036-4/}
}
TY  - JOUR
AU  - Fošner, Ajda
AU  - Šemrl, Peter
TI  - Spectrally Bounded Linear Maps on $B\text{(X)}$
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 369
EP  - 372
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-036-4/
DO  - 10.4153/CMB-2004-036-4
ID  - 10_4153_CMB_2004_036_4
ER  - 
%0 Journal Article
%A Fošner, Ajda
%A Šemrl, Peter
%T Spectrally Bounded Linear Maps on $B\text{(X)}$
%J Canadian mathematical bulletin
%D 2004
%P 369-372
%V 47
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-036-4/
%R 10.4153/CMB-2004-036-4
%F 10_4153_CMB_2004_036_4

[1] [1] Aupetit, B., Propriétés spectrales des algèbres de Banach. Lecture Notes in Mathematics, 735, Springer-Verlag, Heidelberg 1979. Google Scholar

[2] [2] Aupetit, B., Sur les transformations qui conserve le spectre. Banach Algebras ‘97, E. Albrecht and M. Mathieu, eds., de Gruyter, Berlin, 1998, pp. 55–78. Google Scholar

[3] [3] Aupetit, B., Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras. J. London Math. Soc. 62 (2000), 917–924. Google Scholar

[4] [4] Brešar, M. and Šemrl, P., Linear maps preserving the spectral radius, J. Funct. Anal. 142 (1996), 360–368. Google Scholar

[5] [5] Dales, H. G., Loy, R. J. and Willis, G. A., Homomorphisms and derivations from B(E), J. Funct. Anal. 120 (1994), 201–219. Google Scholar

[6] [6] Kaplansky, I., Algebraic and analytic aspects of operator algebras. American Mathematical Society, Providence, RI, 1970. Google Scholar

[7] [7] Mathieu, M., Spectrally bounded traces on C*-algebras. Bull. austral. Math. 68 (2003), 169–173. Google Scholar

[8] [8] Mathieu, M. and Schick, G. J., First results on spectrally bounded operators. Studia Math. 152 (2002), 187–199. Google Scholar

[9] [9] Mathieu, M. and Schick, G. J., Spectrally bounded operators from von Neumann algebras. J. Operator Theory, 49(2003) 285–293. Google Scholar

[10] [10] Mityagin, B. S. and Edelhstein, I. S., Homotopy type of linear groups for two classes of Banach spaces, Funkcional. Anal. i Priložen. 4 (1970), 61–72 (in Russian). Google Scholar

[11] [11] Šemrl, P., Linear maps that preserve the nilpotent operators, Acta Sci. Math. (Szeged) 61 (1995), 523–534. Google Scholar

[12] [12] Šemrl, P., Spectrally bounded linear maps on B(H), Quart. J. Math. Oxford 49 (1998), 87–92. Google Scholar

[13] [13] Wilansky, A., Subalgebras of B(X), Proc. Amer.Math. Soc. 29 (1971), 355–360. Google Scholar

Cité par Sources :