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

No Thumbnail Available

##### Issue Date

July 2018

##### Authors

Kaneda, Masayoshi

##### Keywords

##### Type

Journal Article

Peer-Reviewed

Peer-Reviewed

##### Abstract

We define an -TRO as an off-diagonal corner of an-algebra, and show that the unit ball of an -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 -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 -algebra (respectively, an injective-algebra). In particular, we observe that an-TRO, hence an injective operator space, has an algebrization which admits a quasi-identity.