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

Volume 215 / 2013

H. Najafi, M. S. Moslehian Studia Mathematica 215 (2013), 31-37 MSC: Primary 46L05; Secondary 46L10. DOI: 10.4064/sm215-1-3

Abstract

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.

Authors

  • H. NajafiDepartment of Pure Mathematics
    Center of Excellence in Analysis on Algebraic Structures (CEAAS)
    Ferdowsi University of Mashhad
    P.O. Box 1159
    Mashhad 91775, Iran
    e-mail
  • M. S. MoslehianDepartment of Pure Mathematics
    Center of Excellence in Analysis on Algebraic Structures (CEAAS)
    Ferdowsi University of Mashhad
    P.O. Box 1159
    Mashhad 91775, Iran
    e-mail
    e-mail

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