On operators with closed ranges
Tóm tắt
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 A1/2 have the same range if and only if A has closed range and of Banach’s closed range theorem for Hilbert space operators.
Tài liệu tham khảo
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