The Banach-Lie algebra of multiplication operators on a JBW-triple |
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Authors: | Najla A. Altwaijry |
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Affiliation: | The Queen's College, Oxford, United Kingdom |
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Abstract: | The Banach-Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is shown that the hermitian part Lh(A) of L(A) is a unital GM-space the base of the dual cone in the dual GL-space ∗(Lh(A)) of which is affine isomorphic and weak∗-homeomorphic to the state space of L(A). In the case in which A is a JBW∗-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space Lh(A) satisfy 0?D(u,u)+D(v,v)?idA, |
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Keywords: | JB&lowast -triple JBW&lowast -triple Multiplication operator |
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