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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Complete continuity of the inverse of a positive symmetric operator.

Author: James P. Fink
Journal: Proc. Amer. Math. Soc. 25 (1970), 147-150
MSC: Primary 47.45
MathSciNet review: 0257797
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Abstract: Let $A$ be a symmetric positive definite linear transformation defined on a dense subset of a Hilbert space $H$, and let ${H_A}$. be the Hilbert space completion of the domain of $A$ with respect to the inner product ${(u,v)_A} = (Au,v)$. It is shown that the inverse of $A$ is completely continuous on ${H_A}$ if and only if it is completely continuous on $H$.

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Keywords: Linear transformations on Hilbert space, symmetric linear transformation, positive linear transformation, completely continuous linear transformation, inverse transformation, eigenvalues of completely continuous transformations, compact linear transformation
Article copyright: © Copyright 1970 American Mathematical Society