Products of Hermitian operators
HTML articles powered by AMS MathViewer
- by L. J. Gray
- Proc. Amer. Math. Soc. 59 (1976), 123-126
- DOI: https://doi.org/10.1090/S0002-9939-1976-0410446-X
- PDF | Request permission
Abstract:
Let $A$ and $B$ be selfadjoint operators on a Hilbert space. It is shown that $AB$ and $BA$ are not necessarily similar if their null spaces have equal dimension. If $A$ and $B$ are assumed to be Fredholm, then similarity can be established if additional conditions are satisfied.References
- I. C. Gohberg and M. G. Kreĭn, The basic propositions on defect numbers, root numbers and indices of linear operators, Amer. Math. Soc. Transl. (2) 13 (1960), 185–264. MR 0113146
- Heydar Radjavi and James P. Williams, Products of self-adjoint operators, Michigan Math. J. 16 (1969), 177–185. MR 244801 A. E. Taylor, Functional analysis, Wiley, New York, 1967.
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 123-126
- MSC: Primary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1976-0410446-X
- MathSciNet review: 0410446