Nihonkai Mathematical Journal

The Radon-Nikodym theorem for non-commutative $L^{p}$-spaces

Hideaki Izumi

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Abstract

Let $\cal M$ be a von Neumann algebra. We will show that for two normal semifinite faithful weights $\phi$, $\psi$ on $\cal M$, the corresponding non-commutative $L^p$-spaces $L^p({\cal M},\phi)$ and $L^p({\cal M},\psi)$ are isometrically isomorphic.

Article information

Source
Nihonkai Math. J., Volume 19, Number 2 (2008), 137-150.

Dates
First available in Project Euclid: 18 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1363634625

Mathematical Reviews number (MathSciNet)
MR2490134

Zentralblatt MATH identifier
1196.46049

Subjects
Primary: 46L51: Noncommutative measure and integration 46L52: Noncommutative function spaces 47L20: Operator ideals [See also 47B10]

Keywords
Modular theory non-commutative integration Connes' Radon-Nikodym cocycle complex interpolation

Citation

Izumi, Hideaki. The Radon-Nikodym theorem for non-commutative $L^{p}$-spaces. Nihonkai Math. J. 19 (2008), no. 2, 137--150. https://projecteuclid.org/euclid.nihmj/1363634625


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References

  • J. Bergh and J. Löfström, Interpolation Spaces: an Introduction, Springer-Verlag, 1976.
  • A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190.
  • A. Connes, Caractérisation des espaces vectoriels ordonnés sous-jacent aux algèbres de von Neumann, Ann. Inst. Fourier 24 (1974), 121–155.
  • U. Haagerup, $L^p$-spaces associated with an arbitrary von Neumann algebra, Colloques Internationaux CNRS, No.274, 175–184.
  • H. Izumi, Constructions of non-commutative $L^p$-spaces with a complex parameter arising from modular actions, Int. J. Math. 8 (1997), 1029–1066.
  • H. Izumi, Natural bilinear forms, natural sesquilinear forms and the associated duality of non-commutative $L^p$-spaces, Int. J. Math. 9 (1998), 975–1039.
  • H. Kosaki, Applications of the Complex Interpolation Method to a von Neumann Algebra: Non-commutative $L^p$-Spaces, J. Funct. Anal. 56 (1984), 29–78.
  • S. Strătilă, Modular Theory in Operator Algebras, Abacus Press, 1981.
  • M. Takesaki, Theory of Operator Algebras II, Springer-Verlag, 2003.
  • M. Terp, Interpolation spaces between a von Neumann algebra and its predual, J. Operator Theory 8 (1982), 327–360.