کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616156 1339340 2014 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Active lattices determine AW*-algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Active lattices determine AW*-algebras
چکیده انگلیسی

We prove that operator algebras that have enough projections are completely determined by those projections, their symmetries, and the action of the latter on the former. This includes all von Neumann algebras and all AW*-algebras. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-algebras and that of piecewise complete Boolean algebras, and a refinement of the piecewise algebra structure of an AW*-algebra that enables recovering its total structure.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 416, Issue 1, 1 August 2014, Pages 289–313
نویسندگان
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