Page 1

Displaying 1 – 7 of 7

Showing per page

On complete-cocomplete subspaces of an inner product space

David Buhagiar, Emmanuel Chetcuti (2005)

Applications of Mathematics

In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space S is complete if and only if there exists a σ -additive state on C ( S ) , the orthomodular poset of complete-cocomplete subspaces of S . We then consider the problem of whether every state on E ( S ) , the class of splitting subspaces of S , can be extended to a Hilbertian state on E ( S ¯ ) ; we show that for the dense hyperplane S (of a separable Hilbert space) constructed by P. Pták and...

Currently displaying 1 – 7 of 7

Page 1