Rocky Mountain Journal of Mathematics

Bilinear integration and applications to operator and scattering theory

Brian Jefferies

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We show how to integrate operator valued functions with respect to a spectral or orthogonally scattered measure. Such measures typically have a variation which has either the value zero or infinity on any set and cannot therefore be treated by the approaches of Bartle or Dobrakov. Bilinear integrals of this type arise from trace class operators between Banach function spaces and in the connection between stationary-state scattering theory and time-dependent scattering theory in Hilbert space.

Article information

Rocky Mountain J. Math., Volume 46, Number 1 (2016), 189-225.

First available in Project Euclid: 23 May 2016

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Zentralblatt MATH identifier

Primary: 28A25: Integration with respect to measures and other set functions 46A32: Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
Secondary: 46N50: Applications in quantum physics

Bilinear integral trace class operator nuclear operator trace spectral measure


Jefferies, Brian. Bilinear integration and applications to operator and scattering theory. Rocky Mountain J. Math. 46 (2016), no. 1, 189--225. doi:10.1216/RMJ-2016-46-1-189.

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