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- W2112113398 abstract "We demonstrate that all JB ∗ -triples (hence, all JB ∗ -algebras and all C ∗ -algebras) are non-degenerate Jordan triple systems but a Jordan triple system may not be non-degenerate; any two elements x and y in a non-degenerate Jordan triple system are von Neumann regular with generalized inverses of each other whenever the induced Bergmann operator B(x,y) (or equivalently, B(y,x)) vanishes; however, the converse is not true even in case of C ∗ -algebras. L. G. Brown and G. K. Pedersen introduced a notion of quasi-invertible elements in a C ∗ -algebra, which plays a significant role in studying geometry of the unit ball. Recently, the present authors began a study of BP-quasi invertible elements in the general setting of JB ∗ -triples; here, it is deduced further that B(x,y) on a JB ∗ -triple J vanishes if and only if x and y are BP-quasi inverses of each other. Thus, von Neumann regularity for BP-quasi invertible elements in a JB ∗ -triple is a necessity but not a sufficiency." @default.
- W2112113398 created "2016-06-24" @default.
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- W2112113398 date "2011-01-01" @default.
- W2112113398 modified "2023-09-28" @default.
- W2112113398 title "On Non-degenerate Jordan Triple Systems" @default.
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