Geodesic
Deformation of involution and multiplication in a $C^*$-algebra
H. Najafi1 ; M. S. Moslehian1
1 Department of Pure Mathematics Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad P.O. Box 1159 Mashhad 91775, Iran
Studia Mathematica, Tome 215 (2013) no. 1, pp. 31-37 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm215-1-3
Keywords: investigate deformations involution multiplication unital * algebra its norm fixed main result present multiplications involutions given * algebra mathcal under which mathcal still * algebra keep norm unchanged each invertible element mathcal introduce involution multiplication making mathcal * algebra which becomes positive element further necessary sufficient condition center unital * algebra mathcal trivial

H. Najafi 1 ; M. S. Moslehian 1

1 Department of Pure Mathematics Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad P.O. Box 1159 Mashhad 91775, Iran 
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H. Najafi; M. S. Moslehian. Deformation of involution and multiplication in a $C^*$-algebra. Studia Mathematica, Tome 215 (2013) no. 1, pp. 31-37. doi: 10.4064/sm215-1-3

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