arXiv 2201.045092022-01math.OAmath.FA

Isomorphisms of spectral lattices

Martin Bohata

备注：: Some misprints were corrected and references were updated

英文摘要：

The paper deals with spectral order isomorphisms between certain spectral sublattices of direct sums of AW*-factors. We prove that these maps consist of spectral order isomorphisms between spectral sublattices of individual direct summands. Consequently, we obtain a complete description of spectral order isomorphisms in the case of atomic AW*-algebras. This includes the setting of matrix algebras. Moreover, we also exhibit the general form of spectral order orthoisomorphisms between various spectral sublattices of direct sums of AW*-factors.

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