AUTOMATIC CONTINUITY OF ALMOST MULTIPLICATIVE LINEAR FUNCTIONALS ON FRÉCHET ALGEBRAS

Title & Authors
AUTOMATIC CONTINUITY OF ALMOST MULTIPLICATIVE LINEAR FUNCTIONALS ON FRÉCHET ALGEBRAS
Honary, Taher Ghasemi; Omidi, Mashaallah; Sanatpour, Amir Hossein;

Abstract
A linear functional T on a $\small{Fr{\acute{e}}echet}$ algebra (A, (pn)) is called almost multiplicative with respect to the sequence ($\small{p_n}$), if there exists $\small{{\varepsilon}{\geq}0}$ such that $\small{{\mid}Tab-TaTb{\mid}{\leq}{\varepsilon}p_n(a)p_n(b)}$ for all $\small{n{\in}\mathbb{N}}$ and for every $\small{a,b{\in}A}$. We show that an almost multiplicative linear functional on a $\small{Fr{\acute{e}}echet}$ algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous $\small{Fr{\acute{e}}echet}$ algebra is continuous.
Keywords
multiplicative maps (homomorphisms);almost multiplicative maps;almost multiplicative linear functionals;automatic continuity;$\small{Fr{\acute{e}}echet}$ algebras;Q-algebras;
Language
English
Cited by
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