Abstract

Let $I$ be a real interval and $X$ be a Banach space. It is observed that spaces $\Lambda BV^{(p)}([a, b],R)$, $LBV(I,X)$ (locally bounded variation), $BV_0(I,X)$ and $LBV_0(I,X)$ share many properties of the space $BV([a,b],R)$. Here we have proved that the space $\Lambda BV^{(p)}_0(I,X)$ is a Banach space with respect to the variation norm and the variation topology makes $L\Lambda BV^{(p)}_0(I,X)$ a complete metrizable locally convex vector space (i.e\. a Fréchet space).

Keywords: $\Lambda BV^{(p)}$; Banach space; complete metrizable locally convex vector space; Fréchet space.

MSC: 26A45, 46A04

Pages:  47$-$50     

Volume  62 ,  Issue  1 ,  2010