automatic continuity of almost multiplicative maps between frechet algebras

نویسندگان

t. ‎ghasemi honary‎

department of‎ ‎mathematics, ‎kharazmi university‎, ‎1561836314, tehran‎, ‎iran m. omidi

department of‎ ‎mathematics, ‎kharazmi university‎, ‎1561836314, tehran‎, ‎iran a. h. sanatpour

department of‎ ‎mathematics, ‎kharazmi university‎, ‎1561836314, tehran‎, ‎iran

چکیده

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.

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Automatic continuity of almost multiplicative maps between Frechet algebras

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عنوان ژورنال:
bulletin of the iranian mathematical society

جلد ۴۱، شماره ۶، صفحات ۱۴۹۷-۱۵۰۹

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