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Deformation of involution and multiplication in a $C^*$-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.

Autorzy

• H. NajafiDepartment of Pure Mathematics
Center of Excellence in Analysis on Algebraic Structures (CEAAS)
P.O. Box 1159
e-mail
• M. S. MoslehianDepartment of Pure Mathematics
Center of Excellence in Analysis on Algebraic Structures (CEAAS)