Characterizations of Lie derivations on Kadison-Singer algebras

被引：1

作者：

An, Guangyu ^{[1
]}

Zhang, Rui ^{[1
]}

He, Jun ^{[2
]}

Cheng, Xing ^{[1
]}

机构：

[1] Shaanxi Univ Sci & Technol, Xian 710021, Peoples R China

[2] Anhui Polytech Univ, Wuhu 241000, Peoples R China

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2023年 / 17卷 / 03期

关键词：

Lie derivation; Derivation; Kadison-Singer lattice; Kadison-Singer algebra; Nest algebra;

D O I：

10.1007/s43037-023-00282-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Kadison-Singer algebra (KS-algebra) is a new class of non-self-adjoint operator alge-bras. In this paper, we mainly study the standardization of Lie derivations on some KS-algebras. In Sect. 2, we prove that if L is a non-trivial KS-lattice in M-3(C) , then every Lie derivation from AlgL into M-3(C) is standard. In Sect. 3, we suppose that H is a separable infinite-dimensional Hilbert space, N is a non-trivial nest on H and ? is a separating vector for N". Let L be a KS-lattice generated by N and the rank-one projection P-? , we prove that every Lie derivation from AlgL into B(H) is standard.

引用

页数：22

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