On the facial structure of the unit ball in the dual space of a JB*-triple |
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Authors: | Francisco J Fernández-Polo Antonio M Peralta |
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Institution: | 1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain
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Abstract: | It is shown that every proper weak* closed face of the closed unit ball E1*{E_1^*} in the dual space of a JB*-triple E coincides with set of all elements in the unit sphere of E* attaining their norm at a unique compact tripotent in E**. In particular every proper weak* closed face of the closed unit ball E1*{E_1^*} is weak*-semi-exposed. This result provides an affirmative answer to a conjecture posed over 20 years ago. |
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