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Another positivity result for determinantal operators

Published online by Cambridge University Press:  14 November 2011

Paul Binding
Paul Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Alberta, Canada T2N 1N4 and Control Theory Centre, University of Warwick, Coventry, EnglandCV4 7 AL
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Synopsis

Let Vrs, s = 1 … k, be Hermitian operators on separable Hilbert spaces Hr, r = 1 … k. For x⊗ = x1⊗ … ⊗ xk ∈ H = H1⊗…Δx⊗ by the formal determinantal expansion ⊗ det [Vrsxr Δ is then extended by linearity and continuity to H. It is shown that a positive definiteness condition on Δ need be checked only for decomposable tensors like x⊗. Applications are given to several conditions in the multiparameter eigenvalue literature.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 3-4 , 1980 , pp. 333 - 337
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

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