MULTIPLICATIVE PRIMENESS OF COMPLEXIFICATION FOR REAL ALGEBRAS

Characterizations of peripherally multiplicative mappings between real function algebras

Let X be a compact Hausdorff space; let τ : X → X be a topological involution; and let A ⊂ C(X, τ) be a real function algebra. Given an f ∈ A, the peripheral spectrum of f is the set σπ(f) of spectral values of f of maximum modulus. We demonstrate that if T1, T2 : A → B and S1, S2 : A → A are surjective mappings between real function algebras A ⊂ C(X, τ) and B ⊂ C(Y, φ) that satisfy σπ(T1(f)T2(...

CONTINUITY IN FUNDAMENTAL LOCALLY MULTIPLICATIVE TOPOLOGICAL ALGEBRAS

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

Almost n-Multiplicative Maps‎ between‎ ‎Frechet Algebras

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

Multiplicative bijective maps on standard operator algebras

Automatic continuity of almost multiplicative maps between Frechet algebras

For Fr$acute{mathbf{text{e}}}$chet algebras $(A, (p_n))$ and $(B, (q_n))$, a linear map $T:Arightarrow B$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(Tab - Ta Tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{N}$, $a, b in A$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$...