Abstract
Consider an arbitrary Hilbert space H endowed with a continuous product which induces a grading on H with respect to an abelian group G. We show that such a space H has the form H=cl(U+∑jIj) with U a closed subspace of H1 (the factor associated to the unit element in G), and any Ij a well described closed graded ideal of H, satisfying IjIk=0 if j≠k. Under certain conditions, the graded simplicity of H is characterized and it is shown that H is the closure of the orthogonal direct sum of the family of its minimal (closed) graded ideals, each one being a graded simple graded Hilbert space.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.