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Products of Hermitian operators

Author: L. J. Gray
Journal: Proc. Amer. Math. Soc. 59 (1976), 123-126
MSC: Primary 47B15
MathSciNet review: 0410446
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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.

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  • [1] I. C. Gohberg and M. G. Kreĭn, The basic propositions on defect numbers, root numbers and indices of linear operators, Uspehi Mat. Nauk 12 (1957), no. 2 (74), 43-118; English transl., Amer. Math. Soc. Transl. (2) 13 (1960), 185-264. MR 20 #3459; 22 #3984. MR 0113146 (22:3984)
  • [2] H. Radjavi and J. P. Williams, Products of self-adjoint operators, Michigan Math. J. 16 (1969), 177-185. MR 39 #6115. MR 0244801 (39:6115)
  • [3] A. E. Taylor, Functional analysis, Wiley, New York, 1967.

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Keywords: Hilbert space, products of Hermitians, similarity, Fredholm operators
Article copyright: © Copyright 1976 American Mathematical Society

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