Far Eastern Mathematical Journal

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Lattice normed lattices with monotonically complete and order semicontinuous norm


V. I. Chilin, M. M. Yusupova

2014, issue 2, Ń. 280–296


Abstract
The topological and order properties of the lattice normed lattices (LNL) with monotonically complete and order semicontinuous norm, taking their values in extended Kantorovich – Pinsker spaces, are studied. It is proved the “vector” variant of Abramovich theorem, giving the criterion of $(bo)$-completeness of LNL.

Keywords:
lattice normed lattice, conditions $(B)$ and $(C)$, disjoint decomposable norm

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References

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