Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1970-0257797-4
MathSciNet review: 0257797
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47.45

Retrieve articles in all journals with MSC: 47.45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0257797-4
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