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An n-homomorphism between algebras is a linear map $phi : A to B$ such that $phi(a_1 ... a_n) = phi(a_1)... phi(a_n)$ for all elements $a_1, >..., a_n in A.$ Every homomorphism is an n-homomorphism, for all n >= 2, but the converse is false, in general. Hejazian et al. [7] ask: Is every *-preserving n-homomorphism between C*-algebras continuous? We answer their question in the affirmative, but the even and odd n arguments are surprisingly disjoint. We then use these results to prove stronger ones: If n >2 is even, then $phi$ is just an ordinary *-homomorphism. If n >= 3 is odd, then $phi$ is a difference of two orthogonal *-homomorphisms. Thus, there are no nontrivial *-linear n-homomorphisms between C*-algebras.
Let $G$ be a locally compact group. It is not always the case that its reduced C*-algebra $C^*_r(G)$ admits a tracial state. We exhibit closely related necessary and sufficient conditions for the existence of such. We gain a complete answer when $G$
Given a C$^*$-correspondence $X$, we give necessary and sufficient conditions for the tensor algebra $mathcal T_X^+$ to be hyperrigid. In the case where $X$ is coming from a topological graph we obtain a complete characterization.
We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^*$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^*$-algebras of finite acyclic graphs and finite cycle
We study two classes of operator algebras associated with a unital subsemigroup $P$ of a discrete group $G$: one related to universal structures, and one related to co-universal structures. First we provide connections between universal C*-algebras t
The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the differentiability of thes