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Non-commutative Banach function spaces

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References

  • [CR] Chong, K.M., Rice, N.M.: Equimeasurable rearrangements of functions. Queen's Papers in Pure and Applied Mathematics, no. 28, Queen's University, Kingston (1971)

    Google Scholar 

  • [D] Dixmier, J.: Von Neumann Algebras. Mathematical Libary, vol. 27. Amsterdam: North Holland 1981

    Google Scholar 

  • [DP] Dodds, P.G., Pagter, B. de: Non-commutative Banach function spaces and their duals, Semester Bericht Functionanalysis, Tübingen, Wintersemester, 1988

  • [F] Fack, T.: Sur la notion de valeur caractéristique. J. Oper. Theory7, 307–333 (1982)

    Google Scholar 

  • [FK] Fack, T., Kosaki, H.: Generalizeds-numbers of τ-measurable operators. Pac. J. Math.123, 269–300 (1986)

    Google Scholar 

  • [GK] Gohberg, I.C., Krein, M.G.: Introduction to the theory of linear non-selfadjoint operators, Translations of Mathematical Monographs, vol. 18, AMS (1969)

  • [G] Grothendieck, A.: Réarrangements de fonctions et inégalités de convexité dans les algèbres de von Neumann munies d'une trace, Séminaire Bourbaki (1955), 113-01-113-13

  • [HN] Hiai, F., Nakamura, Y.: Majorizations for generalizeds-numbers in semifinite von Neumann algebras. Math. Z.195, 17–27 (1987)

    Google Scholar 

  • [K] Kosaki, H.: Non-commutative Lorentz spaces associated with a semi-finite von Neumann algebra and applications. Proc. Jap. Acad., Ser. A57, 303–306 (1981)

    Google Scholar 

  • [KPS] Krein, S.G., Petunin, Ju.I., Semenov, E.M.: Interpolation of linear operators, Translations of Mathematical Monographs, vol. 54, AMS (1982)

  • [KR] Kadison, R.V., Ringrose, J.R.: Fundamentals of the theory of operator algebras, vol. I. New York: Academic Press 1983

    Google Scholar 

  • [L] Luxemburg, W.A.J.: Rearrangement invariant Banach function spaces, Queen's Papers in Pure and Applied Mathematics, no. 10, 83–144 (1967)

    Google Scholar 

  • [LS] Lorentz, G.G., Shimogaki, T.: Interpolation theorems for operators in function spaces. J. Funct. Anal.2, 31–51 (1968)

    Google Scholar 

  • [M] Markus, A.S.: The eigen- and singular values of the sum and product of linear operators. Russ. Math. Surv.19, 91–120 (1964)

    Google Scholar 

  • [N] Nelson, E.: Notes on non-commutative integration. J. Funct. Anal.15, 103–116 (1974)

    Google Scholar 

  • [P] Petz, D.: Spectral scale of self-adjoint operators and trace inequalities. J. Math. Anal. Appl.109, 74–82 (1985)

    Google Scholar 

  • [T] Terp, M.:L p-spaces associated with von Neumann algebras, Notes, Copenhagen Univ. (1981)

  • [Y1] Yeadon, F.J.: Non-commutativeL p>-spaces. Math. Proc. Camb. Philos. Soc.77, 91–102 (1975)

    Google Scholar 

  • [Y2] Yeadon, F.J.: Ergodic theorems for semifinite von Neumann algebras: II, Math. Proc. Camb. Philos. Soc.88, 135–147 (1980)

    Google Scholar 

  • [Z1] Zaanen, A.C.: Integration. Amsterdam: North-Holland 1967

    Google Scholar 

  • [Z2] Zaanen, A.C.: Riesz spaces II. Amsterdam: North-Holland 1983

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, The Flinders University of South Australia, 5042, Bedford Park, SA, Australia

    Peter G. Dodds & Theresa K. -Y. Dodds

  2. Department of Mathematics, Delft University of Technology, Julianalaan 132, NL-2628 BL, Delft, The Netherlands

    Ben de Pagter

Authors
  1. Peter G. Dodds
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  2. Theresa K. -Y. Dodds
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  3. Ben de Pagter
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Dedicated to A.C. Zaanen on the occasion of his 75th birthday

Supported by A.R.G.S.

Supported by A.R.G.S. and by the Netherlands Organization for Scientific Research (NWO)

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Dodds, P.G., Dodds, T.K.Y. & de Pagter, B. Non-commutative Banach function spaces. Math Z 201, 583–597 (1989). https://doi.org/10.1007/BF01215160

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