TY - JOUR ID - 711 TI - Automatic continuity of almost multiplicative maps between Frechet algebras JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - ‎Ghasemi Honary‎, T. AU - Omidi, M. AU - Sanatpour, A. H. AD - Department of‎ ‎Mathematics, ‎Kharazmi University‎, ‎1561836314, Tehran‎, ‎Iran AD - Department of‎ ‎Mathematics, ‎Kharazmi University‎, ‎1561836314, Tehran‎, ‎Iran Y1 - 2015 PY - 2015 VL - 41 IS - 6 SP - 1497 EP - 1509 KW - ‎Automatic continuity‎ KW - ‎Fr$acute{text{e}}$chet‎ ‎algebras‎ KW - ‎$Q$-algebras‎ KW - almost multiplicative maps‎ KW - weakly almost‎ ‎multiplicative maps‎ KW - dense range almost‎ ‎multiplicative maps DO - N2 - 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. UR - http://bims.iranjournals.ir/article_711.html L1 - http://bims.iranjournals.ir/article_711_6fbfa2598e04c4a02cb5f3b4852f8f07.pdf ER -