arXiv subjects

S. Hejazian

Publications and source records attributed to S. Hejazian.

3 recordsLinked to original sources

arXiv2007

Achievement of continuity of $(ϕ,ψ)$-derivations without continuity

Suppose that $\calak$ is a $C^*$-algebra acting on a Hilbert space $\calhk$, and that $ϕ, ψ$ are mappings from $\calak$ into $B(\calhk)$ which are not assumed to be necessarily linear or continuous. A $(ϕ, ψ)$-derivation is a linear mapping $d: \calak \to B(\calhk)$ such that $$d(ab)=ϕ(a)d(b)+d(a)ψ(b)\quad (a,b\in \calak).$$ We prove that if $ϕ$ is a multiplicative (not necessarily linear) $*$-mapping, then every $*$-$(ϕ,ϕ)$-derivation is automatically continuous. Using this fact, we show that every $*$-$(ϕ,ψ)$-derivation $d$ from $\calak$ into $B(\calhk)$ is continuous if and only if the $*$-mappings $ϕ$ and $ψ$ are left and right $d$-continuous, respectively.

math.FA↗

arXiv2005

n-Homomorphisms

Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map $ϕ:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $ϕ(a_{1}... a_{n})=ϕ(a_{1})...ϕ(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In this paper, we investigate $n$-homomorphisms and their relation to homomorphisms. We characterize $n$-homomorphisms in terms of homomorphisms under certain conditions. Some results related to continuity and commutativity are given as well.

math.FA↗

arXiv2004

Generalized Induced Norms

Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.

math.FA↗