کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425000 1633785 2016 78 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On operator-valued bi-free distributions
ترجمه فارسی عنوان
بر روی توزیعهای بدون توزیع ارزش اپراتور
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

In this paper, operator-valued bi-free distributions are investigated. Given a subalgebra D of a unital algebra B, it is established that a two-faced family Z is bi-free from (B,Bop) over D if and only if certain conditions relating the B-valued and D-valued bi-free cumulants of Z are satisfied. Using this, we verify that a two-faced family of matrices is R-cyclic if and only if they are bi-free from the scalar matrices over the scalar diagonal matrices. Furthermore, the operator-valued bi-free partial R-, S-, and T-transforms are constructed. New proofs of results from free probability are developed in order to facilitate many of these bi-free results.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 303, 5 November 2016, Pages 638-715
نویسندگان
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