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)

 

 

Absolute continuity of eigenvectors of time-varying operators


Author: Andrew F. Acker
Journal: Proc. Amer. Math. Soc. 42 (1974), 198-201
MSC: Primary 47B05
DOI: https://doi.org/10.1090/S0002-9939-1974-0326457-7
MathSciNet review: 0326457
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ K(t)$ is a compact, selfadjoint operator function of a real variable t with distinct eigenvalues at each t, we show that the eigenvalues and eigenvectors are absolutely continuous and that $ \{ K(t)\} $ is a commuting set provided that $ K(t)$ commutes with its time derivative $ K'(t)$ at each t. The distinct eigenvalue condition is shown to be necessary.


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

  • [1] A. Acker, Stability results for linear systems involving a time varying unbounded operator, Doctoral Dissertation, Boston University, 1972, Appendix B.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B05

Retrieve articles in all journals with MSC: 47B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0326457-7
Keywords: Compact operator function, eigenvalue and eigenvector functions, "real'' Hilbert space, selfadjoint, distinct eigenvalues, absolute continuity, commuting set of operators
Article copyright: © Copyright 1974 American Mathematical Society