We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the $C^1$-continuity property of these operators over Sobolev-type spaces of periodic functions.

Ad un'algebra di von Neumann separabile $M$, in forma standard su di uno spazio di Hilbert $H$, si associa la $C^{*}$ algebra ${\mathcal{O}}_M$ definita come la $C^{*}$ algebra ${\mathcal{O}}_{\mathcal{U}\left(M\right)}$ costituita dai punti fissi dell'algebra di Cuntz generalizzata ${\mathcal{O}}_H$ mediante l'azione canonica del gruppo $\mathcal{U}\left(M\right)$ degli unitari di $M$. Si dà una caratterizzazione di ${\mathcal{O}}_M$ nel caso in cui $M$ è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se $\omega$ è uno stato vettoriale normale e fedele di $M$, la restrizione...

We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.

As usual $C\left(X\right)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$. It is well-known that if $X$ and $Y$ are realcompact spaces such that $C\left(X\right)$ and $C\left(Y\right)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C\left(X\right)$determines$X$. The restriction to realcompact spaces stems from the fact that $C\left(X\right)$ and $C\left(\upsilon X\right)$ are isomorphic, where $\upsilon X$ is the (Hewitt) realcompactification of $X$. In this note, a class of locally compact spaces $X$ that includes properly the class of locally compact realcompact spaces is exhibited...

On montre que les fonctions qui opèrent, par composition a gauche, sur l’espace de Besov d’exposant $s$, avec $0\<s\<1/q$, dans l’espace euclidien de dimension $n$, sont précisément les fonctions lipschitziennes.

Soient $a_1,...,a_n$ des éléments d’une $b$-algèbre commutative unifère $A$. On définit et étudie un “spectre” de $a=(a_1,...,a_n)$ qui dépend de la croissance des fonctions $u_1\left(s\right),...,u_n\left(s\right)$ de l’égalité spectrale$$(a_1-s_1)u_1\left(s\right)+\cdots +(a_n-s_n)u_n\left(s\right)=1$$près du spectre simultané. À partir des propriétés de ce spectre, on construit un calcul fonctionnel qui, réduit au cas banachique, s’étend à certaines fonctions supposées seulement holomorphes à l’intérieur du spectre simultané. Ce calcul fonctionnel permet aussi d’étudier la régularité des éléments $a_1,...,a_n$ et des fonctions $u_1\left(s\right),...,u_n\left(s\right)$.