Semiclosed operators in Hilbert space

Kaufman, William E.

doi:10.1090/S0002-9939-1979-0534392-9

Semiclosed operators in Hilbert space
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by William E. Kaufman

Proc. Amer. Math. Soc. 76 (1979), 67-73

DOI: https://doi.org/10.1090/S0002-9939-1979-0534392-9

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Abstract:

In a Hilbert space H, an operator C is semiclosed provided that there exists a bounded operator B on H, with range the domain of C, such that CB is bounded. The family of all such operators in H is the smallest family containing all closed operators and itself closed under any one of the following: (1) sums, (2) products, (3) strong limits on domains of closed operators. In fact, every algebraic combination of closed operators in H is the sum of two closed one-to-one operators with the same domain and closed ranges.

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