کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9495484 1335132 2005 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fractal entropies and dimensions for microstates spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Fractal entropies and dimensions for microstates spaces
چکیده انگلیسی
Using Voiculescu's notion of a matricial microstate we introduce fractal dimensions and entropies for finite sets of selfadjoint operators in a tracial von Neumann algebra. We show that they possess properties similar to their classical predecessors. We relate the new quantities to free entropy and free entropy dimension and show that a modified version of free Hausdorff dimension is an algebraic invariant. We compute the free Hausdorff dimension in the cases where the set generates a finite-dimensional algebra or where the set consists of a single selfadjoint. We show that the Hausdorff dimension becomes additive for such sets in the presence of freeness.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 222, Issue 1, 1 May 2005, Pages 217-251
نویسندگان
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