Rocky Mountain Journal of Mathematics

Bilinear integration and applications to operator and scattering theory

Brian Jefferies

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Abstract

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

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

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1464035859

Digital Object Identifier
doi:10.1216/RMJ-2016-46-1-189

Mathematical Reviews number (MathSciNet)
MR3506085

Zentralblatt MATH identifier
1351.28003

Subjects
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

Keywords
Bilinear integral trace class operator nuclear operator trace spectral measure

Citation

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. https://projecteuclid.org/euclid.rmjm/1464035859


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