banach module valued separating maps and automatic continuity

Banach module valued separating maps and automatic continuity

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet 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 $(q_n)$...

Automatic continuity of surjective $n$-homomorphisms on Banach algebras

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

automatic continuity of homomorphisms between banach algebras and frechet algebras

Continuity of Derivations, Intertwining Maps, and Cocycles from Banach Algebras

Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S :AMNE is intertwining if the bilinear map (a, b)PN (δ"S ) (a, b)B a[Sb®S(ab)­Sa[b, A¬AMNE, is continuous, and a linear map D :AMNE is a deriŠation if δ"D ̄ 0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous. The purpose of the present paper is to prove that the continui...