Complementary inner ideals in JBW*-triples

作者：Lubbe Andreas A^*

来源：Journal of Algebra, 2012, 350(1): 36-63.

DOI：10.1016/j.jalgebra.2011.10.027

• JBW*-triple
• Inner ideal
• Complementation
• Complemented
• Peirce inner ideal

The annihilator L-perpendicular to of a subspace L of a JBW*-triple A consists of the elements a in A for which (L a A) is equal to (0), the kernel Ker(L) of L consists of those elements a in A for which {L a L} is equal to (0), and the inner ideal Inid(L) in A associated with L consists of the elements a in A for which {a L a} is equal to (0) and {L a A} is contained in L. A weak*-closed subspace J is said to be an inner ideal in A if {J A J} is contained in J, in which case
A = J circle plus J(1) circle plus J(perpendicular to),
where J(1) is the intersection of the kernels of J and J(perpendicular to). The inner ideal Inid(J) in A associated with a weak*-closed inner ideal J in A forms a complementary weak*-closed inner ideal to J. It turns out that Inid(J) is compatible with J and coincides with Inid(J) boolean AND k(J(perpendicular to perpendicular to)) circle plus(M) J(perpendicular to). In the case where J is a Peirce inner ideal in A, by completely identifying Inid(J), it is shown that Inid(J) is a Peirce inner ideal in A and the inner ideal Inid(Inid(J)) in A associated with Inid(J) is equal to J.

• 出版日期2012-1-15