Some aspects of automatic continuity

SOME RESULTS OF CONTINUITY ?f

The dynamical behavior of a map on the unit interval has been the subject of much contemporary research. In this paper, we will consider the relation between the continuity of the map cof and cof for some positive integer k, where f is a continuous map from the unit interval to itself, and ?f is a function which takes any element of the unit interval to the set of all subsequential limits o...

Automatic Continuity of Higher Derivations on JB*-Algebras

Some Results on Automatic Continuity of Group Representations and Morphisms

In the first part of the paper, some criteria of continuity of representations from a locally compact group in a Banach algebra are given. The common feature of these results is the fact that the continuity of a representation can be deduced from the continuity of its composition with some linear forms on its range. The second part uses the result of the first part to deduce automatic continuit...

Some Linguistic Aspects For Automatic Text Understanding

This paper proposes a system of mapping classes of syntactic structures as instruments for automatic text understanding. The system illustrated in Japanese consists of a set of verb classes and information on mapping them together with noun phrases, tense and aspect. The system. having information on direction of possible inferences between the verb classes with information on tense and aspect,...

Automatic continuity of almost multiplicative maps between Frechet algebras

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 $(q_n)$...