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Abstract. We give domain and range characterization of the smallest (Krein--von Neumann) positive self-adjoint extension of Hilbert space operators. There are given new proofs of these facts for the largest (Friedrichs) extension as well. Boundedly or compactly invertible extremal extensions are also characterized as a result of an application of our treatment.
AMS Subject Classification
(1991): 47A20, 47B25
Keyword(s):
Positive operator,
Friedrichs extension,
Krein--von Neumann extension,
invertible extension
Received October 3, 2001. (Registered under 2898/2009.)
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