A unified approach to infinitesimal freeness with amalgamation

被引：2
|
作者：
Tseng, Pei-Lun [1 ]
机构：
[1] New York Univ Abu Dhabi, Dept Math, Abu Dhabi, U Arab Emirates
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2023年 / 34卷 / 13期
关键词：
OVI freeness; OVI free cumulants; and OVI free convolutions; FREE PROBABILITY; S-TRANSFORM;
D O I：
10.1142/S0129167X23500799
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the infinitesimal freeness in the operator-valued framework, and we show that the operator-valued infinitesimal (OVI) free independence is equivalent to the operator-valued free independence over an algebra of 2 x 2 upper triangular matrices. We introduce the notion of OVI cumulants and investigate its properties, and we then deduce that the OVI freeness is equivalent to the vanishing of our mixed cumulants. Moreover, we derive the formula for obtaining the free additive and multiplicative convolutions within the realm of OVI freeness.
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收藏
页数：26
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