The Banach-Lie Algebra of Multiplication Operators on a JBW*-triple

Journal Article

Altwaijry, N. . 2008

• المجلة \ الصحيفة: Journal of Functional Analysis
• رقم العدد: 254
• الصفحات: 2866–2892

مستخلص المنشور

The Banach–Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is
shown that the hermitian part L(A)h of L(A) is a unital GM-space the base of the dual cone in the dual
GL-space (L(A)h)
∗ 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 L(A)h satisfy
0 D(u, u) +D(v, v) idA,
and that u is a pre-associate of v if and only if
D(u, u) D(v, v).