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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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