On integration with respect to a trace
This chapter discusses integration with respect to a trace. It describes an approach for noncommutative integration, which is based on order. If φ is a faithful semifinite normal trace on the von Neumann algebra a, there is a natural upper integral on the (unbounded) positive self-adjoint operators...
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| Format: | Chapter/Article Conference Paper |
| Language: | English |
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28 April 2008
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| In: |
Aspects of positivity in functional analysis
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| DOI: | 10.1016/S0304-0208(08)71962-5 |
| Subjects: | |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1016/S0304-0208(08)71962-5 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0304020808719625 
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| Author Notes: | Michael Leinert |
| Summary: | This chapter discusses integration with respect to a trace. It describes an approach for noncommutative integration, which is based on order. If φ is a faithful semifinite normal trace on the von Neumann algebra a, there is a natural upper integral on the (unbounded) positive self-adjoint operators affiliated with a. The upper integral together with interpolation provides an easy access to the usual results in noncommutative integration. The chapter presents some of the proofs of theorems on integration. The Banach space L1 and the normed sets Lp are discussed in the chapter. Monotone convergence theorem is stated and a discussion on Egoroff's theorem and Dominated convergence theorem is presented in the chapter. The identification of Lp as interpolation space is also discussed in the chapter. |
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| Item Description: | Available online 28 April 2008 Gesehen am 07.06.2018 |
| Physical Description: | Online Resource |
| ISBN: | 9780444879592 0444879595 |
| DOI: | 10.1016/S0304-0208(08)71962-5 |