Functions with values in locally convex spaces with weakly compact semivariation

Year, pages: 2012, 133 - 139

The present paper is concerned with some properties of functions with values in locally convex vector spaces, especially functions having weakly compact semivariation and generalizations of some theorems for functions with values in locally convex vector spaces, namely: If $X$ is a sequentially complete locally convex vector space, then the function $x(·)\colon [a,b] \to X$ having a weakly compact semivariation on the interval $[a,b]$ defines a vector valued measure $m$ on Borel subsets of $[a,b]$ with values in $X$ and the range of this measure is a weakly relatively compact subset in $X$. This theorem is an extension of the result of Sirvint and of Edwards from Banach spaces to locally convex spaces.

Duchoň, M., Vadovič, P. 2012. Functions with values in locally convex spaces with weakly compact semivariation. In Tatra Mountains Mathematical Publications, vol. 52, no.2, pp. 133-139. 1210-3195.

Duchoň, M., Vadovič, P. (2012). Functions with values in locally convex spaces with weakly compact semivariation. Tatra Mountains Mathematical Publications, 52(2), 133-139. 1210-3195.