The unit ball of an injective operator space has an extreme point
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...
محفوظ في:
| المؤلف الرئيسي: | |
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| منشور في: |
2018
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| الوصول للمادة أونلاين: | http://hdl.handle.net/11675/5107 https://www.sciencedirect.com/science/article/pii/S0022247X18302348 |
| الوسوم: |
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| الملخص: | 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. |
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