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Operator integrals and sesquilinear forms |
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| Authors: | DA Dubin J Kiukas J-P Pellonpää K Ylinen |
| Institution: | 1. Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK;2. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK;3. Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland;4. Department of Mathematics and Statistics, University of Turku, FI-20014 Turku, Finland |
| Abstract: | We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to each other in view of the extension theory of symmetric operators. We demonstrate the associated mathematical subtleties with a physically relevant example involving moment operators of the momentum observable of a particle confined to move on a bounded interval. |
| Keywords: | Vector measure Operator measure Operator integral Sesquilinear form Quantum observable |
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