Semiclosed operators in Hilbert space

Author:
William E. Kaufman

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

MSC:
Primary 47A05

MathSciNet review:
534392

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

Keywords:
Closed operator,
semiclosed operator,
Hilbert space,
complete inner product space,
operator ranges

Article copyright:
© Copyright 1979
American Mathematical Society