Abstract
It is known, by Gelfand theory, that every commutative JB∗-triple admits a representation as a space of continuous functions of the formC0T(L)={a∈C0(L):a(λt)=λa(t),∀λ∈T,t∈L},where L is a principal T-bundle and T denotes the unit circle in C. We provide a full technical description of all orthogonality preserving (non-necessarily continuous nor bijective) linear maps between commutative JB∗-triples. Among the consequences of this representation, we obtain that every linear bijection preserving orthogonality between commutative JB∗-triples is automatically continuous and bi-orthogonality preserving.
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.
