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Positivity results for determinantal operators

Published online by Cambridge University Press:  14 November 2011

Paul Binding  and
Patrick J. Browne
Paul Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Alberta, Canada
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Alberta, Canada
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Synopsis

Let Vrs, s = 1 …, K be Hermitian operators on Hilbert spaces Hr, r = 1, …, k. For x = x1⊗…⊗xk ∊ H1⊗…⊗Hk we define Δx by the formal determinantal expansion Δx = ⊗det{Vrsxr}. Δ is extended to all of H by linearity and continuity. The paper presents results concerning positivity properties of Δ on decomposable tensors.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 3-4 , 1978 , pp. 267 - 271
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Atkinson, F. V.Multiparameter spectral theory. Bull. Amer. Math. Soc. 74 (1968), 1–27.CrossRefGoogle Scholar
2Atkinson, F. V.Multiparameter Eigenvalue Problems. I: Matrices and Compact Operators (New York: Academic Press, 1972).Google Scholar
3Binding, P. and Browne, P. J.A variational approach to multi-parameter eigenvalue problems for matrices. SIAM J. Math. Anal, 8, (1977), 763–777.CrossRefGoogle Scholar
4Borsuk, K.Drei Sätze über die n-dimensionale euklidische Sphäre. Fund. Math. 20 (1933), 177–190.CrossRefGoogle Scholar
5Browne, P. J.Multi-parameter spectral theory. Indiana Univ. Math. J. 24 (1974), 249–257.CrossRefGoogle Scholar
6Källström, A. and Sleeman, B. D.Solvability of a linear operator system. J. Math. Anal. Appl. 55 (1976), 785–793.CrossRefGoogle Scholar
7Sleeman, B. D.Singular linear differential operators with many parameters. Proc. Roy. Soc. Edinburgh Sect. A 71 (1973), 199–232.Google Scholar