Abstract
It is shown that every bounded, unital linear map** that preserves elements of square zero from a C*-algebra of real rank zero and without tracial states into a Banach algebra is a Jordan homomorphism.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Alaminos, M. Brešar, J. Extremera, Š. Špenko and A. R. Villena, Commutators and square-zero elements in Banach algebras, Quart. J. Math., 67 (2016), 1–13.
B. Aupetit, A Primer on Spectral Theory, Springer-Verlag, New York, 1991.
B. Aupetit, Spectrum-preserving linear map**s between Banach algebras or Jordan-Banach algebras, J. London Math. Soc., 62 (2000), 917–924.
B. Blaokadar and D. Handelman, Dimension functions and traces on C*-algebras, J. Funct. Anal., 45 (1982), 297–340.
P. Civin and B. Yood, Lie and Jordan structures in Banach algebras, Pacific J. Math., 15 (1965), 775–797.
Y.-F. Lin and M. Mathieu, Jordan isomorphism of purely infinite C*-algebras, Quart. J. Math., 58 (2007), 249–253.
M. Mathieu, Spectrally bounded operators on simple C*-algebras, Proc. Amer. Math. Soc., 132 (2004), 443–446.
M. Mathieu, Spectrally bounded operators on simple C*-algebras II, Irish Math. Soc. Bull., 54 (2004), 33–40.
M. Mathieu, A collection of problems on spectrally bounded operators, Asian-Eur. J. Math., 2 (2009), 487–501.
M. Mathieu and G. J. Schick, Spectrally bounded operators from von Neumann algebras, J. Operator Theory, 49 (2003), 285–293.
M. Mathieu and A. R. Sourour, Spectral isometries on non-simple C*-algebras, Proc. Amer. Math. Soc., 142 (2014), 129–145.
M. Mathieu and M. Young, Spectral isometries into commutative Banach algebras, Contemp. Math., 645 (2015), 217–222.
C. Pop, Finite sums of commutators, Proc. Amer. Math. Soc., 130 (2002), 3039–3041.
L. Robert, On the Lie ideals of C*-algebras, J. Operator Theor., 75 (2016), 387–408.
E. P. Scarparo, Supramenable groups and partial actions, Ergodic Theory Dynam. System., 37 (2017), 1592–1606.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by L. Molnár
Rights and permissions
About this article
Cite this article
Mathieu, M. Characterizing Jordan homomorphisms. ActaSci.Math. 86, 697–701 (2020). https://doi.org/10.14232/actasm-020-067-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.14232/actasm-020-067-7