Abstract
In the previous chapters, we have shown that homogeneous balls and bounded symmetric domains can be realized as unit balls of JB*-triples. Let X be a complex Banach space with the JB*-triple product. The JB*-triple X is called atomic if it is spanned by its minimal tripotents. It is known that the second dual X** of X is a JBW*-triple i.e., X** is a JB*-triple whose triple product is w*-continuous. Moreover, X can be isometrically embedded into the atomic part of its second dual. Hence, any JB*-triples can be considered as a subtriple of an atomic JBW *-triple.
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© 2005 Springer Science+Business Media New York
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Friedman, Y., Scarr, T. (2005). Classification of JBW *-triple factors. In: Physical Applications of Homogeneous Balls. Progress in Mathematical Physics, vol 40. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8208-8_6
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DOI: https://doi.org/10.1007/978-0-8176-8208-8_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6493-4
Online ISBN: 978-0-8176-8208-8
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