The unit ball of an injective operator space has an extreme point

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Kaneda, Masayoshi¹ 

[1] Amer Univ Kuwait, Dept Math & Nat Sci, Coll Arts & Sci, POB 3323, Safat 13034, Kuwait

关键词: Extreme point;    Injective operator space;    Ternary ring of operators (TRO);    Ideal decomposition;    Quasi-identity;    AW*-algebra;   

DOI  :  10.1016/j.jmaa.2018.03.028

来源: Elsevier

【 摘 要 】

We define an AW*-TRO as an off-diagonal corner of an AW*-algebra, and show that the unit ball of an AW*-TRO has an extreme point. In particular, the unit ball of an injective operator space has an extreme point, which answers a question raised in [8] affirmatively. We also show that an AW*-TRO (respectively, an injective operator space) has an ideal decomposition, that is, it can be decomposed into the direct sum of a left ideal, a right ideal, and a two-sided ideal in an AW*-algebra (respectively, an injective C*-algebra). In particular, we observe that an AW*-TRO, hence an injective operator space, has an algebrization which admits a quasi-identity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free