Glasnik Matematicki, Vol. 35, No.1 (2000), 25-44.
THE MINIMAL INDEX OF A SELF-ADJOINT PENCIL
Paul Binding and Branko Najman
Department of Mathematics and Statistics, University of Calgary,
2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4
e-mail: binding@ucalgary.ca
Abstract. Let A and B be selfadjoint
operators ona Hilbert space H. We define minimal index
ν(A,B)
= min {#negative eigenvalues of A -
λB},
we connect it with various ideas in the literature and we
connect it with formulae used in some recent variational principles.
1991 Mathematics Subject Classification.
15A22, 47A13, 47A56, 49R05.
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