Characterization of $n$-Jordan Homomorphisms on Rings

In this paper, we prove that if $\varphi:\mathcal{R}\longrightarrow\mathcal{R}'$ is an $n$-Jordan homomorphism, where $\mathcal{R}$ has a unit $e$, then the map $a\longmapsto \varphi(e)^{n-2}\varphi(a)$ is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.

Characterization of mixed n-Jordan and pseudo n-Jordan homomorphisms

In this article, a new notion of n-Jordan homomorphism namely the mixed n-Jordan homomorphism is introduced. It is proved that how a mixed (n + 1)-Jordan homomorphism can be a mixed n-Jordan homomorphism and vice versa. By means of some examples, it is shown that the mixed n-Jordan homomorphisms are different from the n-Jordan homomorphisms and the pseudo n-Jordan homomorphisms. As a consequence, it shown that every mixed Jordan homomorphism from Banach algebra A into commutative semisimple Banach algebra B is automatically continuous. Under some mild conditions, every unital pseudo 3-Jordan homomorphism is a homomorphism.

U- S Jordan Homomorphisim of Inverse Semirings

Let S be an inverse semiring, and U be an ideal of S. In this paper, we introduce the concept of U-S Jordan homomorphism of inverse semirings, and extend the result of Herstein on Jordan homomorphisms in inverse semirings.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

On Jordan mappings of inverse semirings

In this paper, the notions of Jordan homomorphism and Jordan derivation of inverse semirings are introduced. A few results of Herstein and Brešar on Jordan homomorphisms and Jordan derivations of rings are generalized in the setting of inverse semirings.

A Characterization of Bi-Jordan Homomorphisms on Banach Algebras

For Banach algebras A and B, we show that if U=A×B is unital and commutative, each bi-Jordan homomorphism from U into a semisimple commutative Banach algebra D is a bihomomorphism.

Linear algebraic proof of Wigner theorem and its consequences

We present new proof of non-bijective Wigner theorem on symmetries of quantum systems using only basic linear algebra. It is based on showing that any non-zero Jordan ∗-homomorphism between matrix algebras preserving rank-one projections is implemented by either a unitary or an anitiunitary map. As a new application we extend hitherto known results on preservers of quantum relative entropy to infinite quantum systems.

A CHARACTERISATION OF 3-JORDAN HOMOMORPHISMS ON BANACH ALGEBRAS

We show that, under special hypotheses, each 3-Jordan homomorphism ${\it\varphi}$ between Banach algebras ${\mathcal{A}}$ and ${\mathcal{B}}$ is a 3-homomorphism.