Representation of a class of locally convex \((M)\)-lattices (Q2469121)

Take \({\mathcal H}\subset \mathbb R_{+}^T\) such that \(\bigcup_{h\in{\mathcal H}}h^{-1}(\{0\})=\emptyset\). Put \(c_0(T,{\mathcal H})=\{\psi\in\mathbb R^T \mid \psi\cdot {\mathcal H}\subset c_0(T)\}\). Furnish \(c_0(T,{\mathcal H})\) with the pointwise order and the topology of the multinorm \((\|\cdot\|_h)_{h\in{\mathcal H}}\), where \(\|\psi\|_h=\|\psi h\|_{\infty}\). The author proves a representation theorem for the weighted spaces \(c_0(T,{\mathcal H})\).