Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-06-06T19:20:03.639Z Has data issue: false hasContentIssue false

Spectrally Bounded Linear Maps on $B\text{(X)}$

Published online by Cambridge University Press:  20 November 2018

Ajda Fošner
Affiliation:
Department of Mathematics, PeF University of Maribor Koroška cesta 160 SI-2000 Maribor Slovenia, e-mail: ajda.fosner@uni-mb.si
Peter Šemrl
Affiliation:
Department of Mathematics University of Ljubljana Jadranska 19 SI-1000 Ljubljana Slovenia, e-mail: peter.semrl@fmf.uni-lj.si
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We characterize surjective linear maps on $B\text{(X)}$ that are spectrally bounded and spectrally bounded below.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Aupetit, B., Propriétés spectrales des algèbres de Banach. Lecture Notes in Mathematics, 735, Springer-Verlag, Heidelberg 1979.Google Scholar
[2] Aupetit, B., Sur les transformations qui conserve le spectre. Banach Algebras ‘97, E. Albrecht and M. Mathieu, eds., de Gruyter, Berlin, 1998, pp. 5578.Google Scholar
[3] Aupetit, B., Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras. J. London Math. Soc. 62 (2000), 917924.Google Scholar
[4] Brešar, M. and Šemrl, P., Linear maps preserving the spectral radius, J. Funct. Anal. 142 (1996), 360368.Google Scholar
[5] Dales, H. G., Loy, R. J. and Willis, G. A., Homomorphisms and derivations from B(E), J. Funct. Anal. 120 (1994), 201219.Google Scholar
[6] Kaplansky, I., Algebraic and analytic aspects of operator algebras. American Mathematical Society, Providence, RI, 1970.Google Scholar
[7] Mathieu, M., Spectrally bounded traces on C*-algebras. Bull. austral. Math. 68 (2003), 169173.Google Scholar
[8] Mathieu, M. and Schick, G. J., First results on spectrally bounded operators. Studia Math. 152 (2002), 187199.Google Scholar
[9] Mathieu, M. and Schick, G. J., Spectrally bounded operators from von Neumann algebras. J. Operator Theory, 49(2003) 285293.Google Scholar
[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), 6172 (in Russian).Google Scholar
[11] Šemrl, P., Linear maps that preserve the nilpotent operators, Acta Sci. Math. (Szeged) 61 (1995), 523534.Google Scholar
[12] Šemrl, P., Spectrally bounded linear maps on B(H), Quart. J. Math. Oxford 49 (1998), 8792.Google Scholar
[13] Wilansky, A., Subalgebras of B(X), Proc. Amer.Math. Soc. 29 (1971), 355360.Google Scholar