Representing a closed operator as a quotient of continuous operators

Kaufman, William E.

doi:10.1090/S0002-9939-1978-0509249-9

Representing a closed operator as a quotient of continuous operators
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by William E. Kaufman PDF

Proc. Amer. Math. Soc. 72 (1978), 531-534 Request permission

Abstract:

The closed operators in a Hilbert space H are characterized as quotients $A{B^{ - 1}}$ of continuous operators on H such that the vector sum ${A^\ast }(H) + {B^\ast }(H)$ is closed. This leads to the function $\Gamma (A) = A{(1 - {A^\ast }A)^{ - 1/2}}$, which is shown to map the strictly contractive operators on H reversibly onto the closed densely-defined operators, so as to preserve the selfadjoint and nonnegative conditions.

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Functional operators