کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592701 1335129 2008 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A dynamical systems approach to the Kadison–Singer problem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A dynamical systems approach to the Kadison–Singer problem
چکیده انگلیسی

In these notes we develop a link between the Kadison–Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the state. We prove that if any state corresponding to a minimal idempotent point extends uniquely to the von Neumann algebra of the group, then every state extends uniquely to the von Neumann algebra of the group. We prove that if any state arising in the Kadison–Singer problem has a unique extension, then the injective envelope of a C*-crossed product algebra associated with the state necessarily contains the full von Neumann algebra of the group. We prove that this latter property holds for states arising from rare ultrafilters and δ-stable ultrafilters, independent, of the group action and also for states corresponding to non-recurrent points in the corona of the group.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 255, Issue 1, 1 July 2008, Pages 120-132