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‎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

Article 19, Volume 41, Issue 6, December 2015, Page 1497-1509  XML PDF (142 K)
Document Type: Research Paper
Authors
T. ‎Ghasemi Honary‎ ; M. Omidi; A. H. Sanatpour
Department of‎ ‎Mathematics, ‎Kharazmi University‎, ‎1561836314, Tehran‎, ‎Iran
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.
Keywords
‎Automatic continuity‎; ‎Fr$acute{text{e}}$chet‎ ‎algebras‎; ‎$Q$-algebras‎; almost multiplicative maps‎; weakly almost‎ ‎multiplicative maps‎; dense range almost‎ ‎multiplicative maps
Main Subjects
46-XX Functional Analysis; 47-XX Operator theory
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