A Completeness Criterion for Inner Product Spaces
Hamhalter, J.; Pták, P.
1987-05-01 00:00:00
We show that a separable inner product space is complete if and only if its lattice of strongly closed subspaces possesses at least one state. This gives a measure‐theoretic characterization of Hilbert spaces among inner product spaces and, as a by‐product, exhibits a ‘continuous’ example of a stateless orthocomplemented lattice.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngBulletin of the London Mathematical SocietyWileyhttp://www.deepdyve.com/lp/wiley/a-completeness-criterion-for-inner-product-spaces-p4oeRWU8VU
We show that a separable inner product space is complete if and only if its lattice of strongly closed subspaces possesses at least one state. This gives a measure‐theoretic characterization of Hilbert spaces among inner product spaces and, as a by‐product, exhibits a ‘continuous’ example of a stateless orthocomplemented lattice.
Journal
Bulletin of the London Mathematical Society
– Wiley
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.