Abstract
The annihilator L ⊥ 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 ⊕ J 1 ⊕ J ⊥ , where J 1 is the intersection of the kernels of J and J ⊥ . 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 ) ∩ k ( J ⊥ ⊥ ) ⊕ M J ⊥ . 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
