Ghasemi Honary, T., Omidi, M., Sanatpour, A. (2015). Automatic continuity of almost multiplicative maps between Frechet algebras. Bulletin of the Iranian Mathematical Society, 41(6), 1497-1509.

T. Ghasemi Honary; M. Omidi; A. H. Sanatpour. "Automatic continuity of almost multiplicative maps between Frechet algebras". Bulletin of the Iranian Mathematical Society, 41, 6, 2015, 1497-1509.

Ghasemi Honary, T., Omidi, M., Sanatpour, A. (2015). 'Automatic continuity of almost multiplicative maps between Frechet algebras', Bulletin of the Iranian Mathematical Society, 41(6), pp. 1497-1509.

Ghasemi Honary, T., Omidi, M., Sanatpour, A. Automatic continuity of almost multiplicative maps between Frechet algebras. Bulletin of the Iranian Mathematical Society, 2015; 41(6): 1497-1509.

Automatic continuity of almost multiplicative maps between Frechet algebras

Receive Date: 07 February 2014,
Revise Date: 03 September 2014,
Accept Date: 19 September 2014

Abstract

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 $(q_n)$, if there exists $varepsilongeq 0$ such that for every $k in mathbb{N}$, there exists $n(k) in mathbb{N}$, satisfying the inequality $q_k(Tab - Ta Tb)leq varepsilon p_{n(k)}(a) p_{n(k)}(b),$ for all $a, b in A$.

We investigate the automatic continuity of (weakly) almost multiplicative maps between certain classes of Fr$acute{mathbf{text{e}}}$chet algebras, such as Banach algebras and Fr$acute{mathbf{text{e}}}$chet $Q$-algebras. We also obtain some results on the automatic continuity of dense range (weakly) almost multiplicative maps between Fr$acute{mathbf{text{e}}}$chet algebras.