Multiplicatively spectrum-preserving maps of function algebras

Spectrum Preserving Linear Maps Between Banach Algebras

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

Multiplicatively Spectrum-preserving and Norm-preserving Maps between Invertible Groups of Commutative Banach Algebras

Let A and B be unital semisimple commutative Banach algebras and T a map from the invertible group A onto B. Linearity and multiplicativity of the map are not assumed. We consider the hypotheses on T : (1) σ(TfTg) = σ(fg); (2) σπ(TfTg−α)∩σπ(fg−α) 6= ∅; (3) r(TfTg−α) = r(fg−α) hold for some non-zero complex number α and for every f, g ∈ A, where σ(·) (resp. σπ(·)) denotes the (resp. peripheral) ...

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

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.

A Survey of Invertibility and Spectrum Preserving Linear Maps

On Preserving Properties of Linear Maps on $C^{*}$-algebras

Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorph...