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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.

MSC:

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