Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503030 | Journal of Mathematical Analysis and Applications | 2005 | 14 Pages |
Abstract
Using recent results on a generalized form of the Loomis-Sikorski theorem [A. DvureÄenskij, Loomis-Sikorski theorem for Ï-complete MV-algebras and â-groups, J. Austral. Math. Soc. Ser. A 68 (2000) 261-277; D. Mundici, Tensor product and the Loomis-Sikorski theorem for MV-algebras, Adv. Appl. Math. 22 (1999) 227-248], it is shown that a unital Dedekind Ï-complete â-group is a compatible Rickart comgroup in the sense of D.J. Foulis [D.J. Foulis, Spectral resolutions in a Rickart comgroup, Rep. Math. Phys. 54 (2004) 229-250]. In particular, elements in unital Dedekind Ï-complete â-groups and, consequently, elements in Ï-MV-algebras, admit uniquely defined spectral resolutions similar to spectral resolutions of self-adjoint operators. A functional calculus and spectra of elements are considered in relation with the Loomis-Sikorski representation by functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
S. Pulmannová,