We investigate the deformations of involution and multiplication in a unital C*-algebra when its norm is fixed. Our main result is to present all multiplications and involutions on a given C*-algebra 𝓐 under which 𝓐 is still a C*-algebra when we keep the norm unchanged. For each invertible element a ∈ 𝓐 we also introduce an involution and a multiplication making 𝓐 into a C*-algebra in which a becomes a positive element. Further, we give a necessary and sufficient condition for the center of a unital C*-algebra 𝓐 to be trivial.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-3,
author = {H. Najafi and M. S. Moslehian},
title = {Deformation of involution and multiplication in a C*-algebra},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {31-37},
zbl = {1280.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-3}
}
H. Najafi; M. S. Moslehian. Deformation of involution and multiplication in a C*-algebra. Studia Mathematica, Tome 215 (2013) pp. 31-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-3/