In: Mathematica Slovaca, vol. 55, no. 2
Surjit Singh Khurana
Detaily:
Rok, strany: 2005, 249 - 252
O článku:
Let $X0$ be a locally compact Hausdorff space, $C0(X0)$ the space of all scalar-valued bounded continuous functions on $X0$ vanishing at infinity, and $X$ a one-point compactification of $X0$. We prove that weak compactness property of unconditionally convergent operators on $C0(X0)$ can be easily deduced by considering the space $C(X)$ and its dual $M(X)$. The result is proved for the vector case $C0(X0,F)$, $F$ being a reflexive Banach space. It is also proved that, for a quasi-complete locally convex space $E$, if $ c0 \nsubseteq E $, then every linear continuous operator $u: C0(X0,F)\to E$ is weakly compact.
Ako citovať:
ISO 690:
Khurana, S. 2005. Unconditionally convergent operators on $C0(X0)$. In Mathematica Slovaca, vol. 55, no.2, pp. 249-252. 0139-9918.
APA:
Khurana, S. (2005). Unconditionally convergent operators on $C0(X0)$. Mathematica Slovaca, 55(2), 249-252. 0139-9918.