Additive maps onto matrix spaces compressing the spectrum

作者：Costara Constantin^*

来源：Journal of Mathematical Analysis and Applications, 2016, 437(2): 1130-1139.

DOI：10.1016/j.jmaa.2016.01.048

• Preserver
• Spectrum
• Additive
• Banach algebras
• Matrix spaces

We prove that given a unital C*-algebra A and an additive and surjective map T : A -> M-n, such that the spectrum of T(x) is a subset of the spectrum of x for each x is an element of A, then T is either an algebra morphism, or an algebra anti-morphism. We arrive at the same conclusion for an arbitrary unital, complex Banach algebra A, by imposing an extra surjectivity condition on the map T.

• 出版日期2016-5-15