Deformation of involution and multiplication in a -algebra
Tom 215 / 2013
Studia Mathematica 215 (2013), 31-37
MSC: Primary 46L05; Secondary 46L10.
DOI: 10.4064/sm215-1-3
Streszczenie
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 \mathcal {A} under which \mathcal {A} is still a C^*-algebra when we keep the norm unchanged. For each invertible element a\in \mathcal {A} we also introduce an involution and a multiplication making \mathcal {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 \mathcal {A} to be trivial.
