Abstract

In this paper, we present some interesting results to characterize the Moore–Penrose inverses of unbounded closable operators and after investigating the Moore–Penrose inverses of the direct sum of closed operators with closed ranges in Hilbert spaces, we establish γ ( T 1 ⨁ T 2 ) = min { γ ( T 1 ) , γ ( T 2 ) } > 0 , where γ ( T ) is the reduced minimum modulus of T.

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