Abstract. We characterize those subpositive operators for which their Krein--von Neumann extension has closed range, moreover we construct their Moore--Penrose inverse. Our treatment follows as a tool the factorization approach to the extension theory of positive operators. As addition we give a short proof of Dixmier's theorem that a bounded positive operator $A$ and its square root $A^{1/2}$ have the same range if and only if $A$ has closed range and of Banach's closed range theorem for Hilbert space operators.
AMS Subject Classification
(1991): 47A20, 47B65, 47A05
Keyword(s):
characterization,
positive operator,
closed range,
Krein--von Neumann extension,
Moore--Penrose inverse
Received December 23, 2009, and in revised form February 1, 2011. (Registered under 6468/2009.)
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