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A Class of Polynomials in Self-Adjoint Operators in Spaces with an Indefinite Metric

Published online by Cambridge University Press:  20 November 2018

C.-Y. Lo
C.-Y. Lo*
Affiliation:
Laurentian University, Sudbury, Ontario
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Let H be a Hilbert space with the usual product [x, y] and with an indefinite inner product (x, y) which, for some orthogonal decomposition

in H, is defined by

where

and dim H1 = κ, a fixed positive integer.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 673 - 678
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This paper is part of the author's Ph.D. thesis supported by the National Research Council of Canada.

References

1. Iohvidov, I. S. and Kreïn, M. G., Spectral theory of operators in spaces with an indefinite metric. I, Transi. Amer. Math. Soc. (2), 13 (1960), 105-176; II, Transi. Amer. Math. Soc. (2), 84 (1963), 283–374.Google Scholar
2. Pontryagin, L. S., Hermitian operators in spaces with indefinite metric, Izv. Akad. Nauk SSSR Ser. Mat, 8 (1944), 243–280. (Russian)Google Scholar