V. I. Chilin, M. M. Yusupova, “Lattice normed lattices with monotonically complete and order semicontinuous norm”, Dal'nevost. Mat. Zh., 2014, Volume 14, Number 2,Pages <nobr>280

Lattice normed lattices with monotonically complete and order semicontinuous norm

V. I. Chilin^a, M. M. Yusupova^b

^a National University of Uzbekistan named after M. Ulugbek, Faculty of Mathematics and Mechanics, Tashkent
^b Gubkin Russian State University of Oil and Gas

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.

Key words: lattice normed lattice, conditions (B) and (C), disjoint decomposable norm.

UDC: 517.98

MSC: Primary 46A19; Secondary 46E30

Received: 01.12.2013