Two Applications of Boolean Valued Analysis

A. G. Kusraev, S. S. Kutateladze

备注：: This a preprint of the work accepted for publication in Siberian Mathematical Journal; $©$ 2019, Pleiades Publishing Ltd. http://pleiades.online/
发表信息：: Siberian Mathematical Journal, 2019, Vol.60, No.5, 902-910
DOI：: 10.1134/S0037446619050124

英文摘要：

The paper contains two main results that are obtained by 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 to the original lattice. The second result establishes a counterpart of the Ando Theorem on the joint characterization of $A\!L^p$ and $c_0$ for the class of cyclic Banach lattices, using the Boolean valued transfer for injective Banach lattices.

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