On extremal positive operator extensions. (English) Zbl 0881.47002

In Theorem 1, the authors describe the domain and the range of the square root of the smallest positive self-adjoint extension (Krein-von Neumann extension) of a positive linear map defined on a linear subspace of a Hilbert space. In Theorem 2, a similar characterization is given concerning the largest positive self-adjoint extension (Friedrichs extension) of a densily defined operator. Finally, Theorem 3 describes the range of the square root of the largest positive extension with the smallest possible norm in case a bounded positive extension exists. The proofs are based on elementary, nevertheless skilful and witty arguments.


47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A20 Dilations, extensions, compressions of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)