Abstract
AbstractC*-algebrasAof compact operators are characterized as those C*-algebras of coefficients of Hilbert C*-modules for which (i) every boundedA-linear operator between two HilbertA-modules possesses an adjoint operator, (ii) the kernels of all bounded A-linear operators between HilbertA-modules are orthogonal summands, (iii) the images of all boundedA-linear operators with closed range between HilbertA-modules are orthogonal summands, and (iv) for every HilbertA-module every HilbertA-submodule is a topological summand. Thus, the theory of Hilbert C*-modules over C*-algebras of compact operators has similarities with the theory of Hilbert spaces. In passing, we obtain a general closed graph theorem for bounded module operators on arbitrary Hilbert C*-modules.
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.
