Remarks on absolute continuity of positive operators

被引：1
|
作者：
Kosaki, Hideki [1 ]
机构：
[1] Kyushu Univ, Grad Sch Math, Nishi Ku, Fukuoka 8190395, Japan
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2023年 / 34卷 / 10期
关键词：
Characteristic matrix; closable part; geometric mean; Hilbert space operator; Lebesgue decomposition; maximal absolutely continuous part; mutual absolute continuity; operator part; parallel sum; positive operator; unbounded operator; LEBESGUE-TYPE DECOMPOSITION; CANONICAL DECOMPOSITION;
D O I：
10.1142/S0129167X23500581
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Ando studied Lebesgue decomposition for (bounded) positive operators, where a notion known as the maximal absolutely continuous part plays a crucial role. Based on technique involving unbounded operators we study certain expressions for the maximal absolutely continuous part, Radon-Nikodym type results, behavior of the maximal absolutely continuous part under the tensor product operation and characterization of mutual absolute continuity and so on.
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页数：28
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