An Extension Theorem for a Sequence of Krein Space Contractions

Abstract EN

Consider Krein spaces U and Y and let Hk and Kk be regular subspaces of U and Y, respectively, such that Hk⊂Hk+1 and Kk⊂Kk+1 (k∈N).

For each k∈N, let Ak:Hk→Kk be a contraction.

We derive necessary and sufficient conditions for the existence of a contraction B:U→Y such that BHk=Ak.

Some interesting results are proved along the way.