Two Applications of Boolean Valued Analysis


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The paper contains two main results that are obtained by using Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector sublattices that are laterally complete and invariant under all band projections and there exists a band preserving linear isomorphism of each of these sublattices onto the original lattice. The second result establishes a counterpart of the Ando Theorem on the joint characterization of ALp and c0 (Γ) for the class of the so-called \(\mathbb{B}\)-cyclic Banach lattices, using the Boolean valued transfer for injective Banach lattices.

作者简介

A. Kusraev

Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences

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Email: kusraev@smath.ru
俄罗斯联邦, Vladikavkaz

S. Kutateladze

Sobolev Institute of Mathematics

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Email: sskut@math.nsc.ru
俄罗斯联邦, Novosibirsk

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