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Two-Dimensional Observables and Spectral Resolutions
Reports on Mathematical Physics ( IF 0.860 ) Pub Date : 2020-04-20 , DOI: 10.1016/s0034-4877(20)30023-9
Anatolij Dvurečenskij; Dominik Lachman

A two-dimensional observable is a special kind of a σ-homomorphism defined on the Borel σ-algebra of the real plane with values in a σ-complete MV-algebra or in a monotone σ-complete effect algebra. A two-dimensional spectral resolution is a mapping defined on the real plane with values in a σ-complete MV-algebra or in a monotone σ-complete effect algebra which has properties similar to a two-dimensional distribution function in probability theory. We show that there is a one-to-one correspondence between two-dimensional observables and two-dimensional spectral resolutions defined on a σ-complete MV-algebras as well as on the monotone σ-complete effect algebras with the Riesz decomposition property. The result is applied to the existence of a joint two-dimensional observable of two one-dimensional observables.
更新日期:2020-04-20

 

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