A Note on Spectrum Preserving Additive Maps on C*-Algebras

Subject Areas : Statistics

Ali Taghavi ¹ (Department of Mathematics, University of Mazandaran, Babolsar, Iran)

Received: 2016-05-25 Accepted : 2016-09-10 Published : 2016-06-21

Keywords: نگاشت جمعی, جبر باناخ, C*- جبر, همریختی جردن, طیف,

Abstract :

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.