Classification of continuous $JBW^ *$-triples
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- by G. Horn and E. Neher PDF
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Abstract:
We show that every $JB{W^{\ast }}$-triple without a direct summand of type I is isometrically isomorphic to an ${l^\infty }$-sum $\mathcal {R}{ \otimes ^\infty }H(A, \alpha )$ where $\mathcal {R}$ is a ${w^{\ast }}$-closed right ideal in a ${W^{\ast }}$-algebra $B$ and $H(A, \alpha )$ are the elements of a ${W^{\ast }}$-algebra $A$ which are symmetric under a C-linear involution $\alpha$ of $A$. Both $A$ and $B$ do not have a direct (${W^{\ast }}$-algebra) summand of type I. In order to refine the decomposition $\mathcal {R}{ \otimes ^\infty }H(A, \alpha )$ we define and characterize types of $JB{W^{\ast }}$-triples.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 306 (1988), 553-578
- MSC: Primary 46L70; Secondary 17C65, 46H70
- DOI: https://doi.org/10.1090/S0002-9947-1988-0933306-7
- MathSciNet review: 933306