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Nehari-Type Theorem for Non-commutative Hardy Spaces

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Abstract

In this paper, we give an answer to a conjecture due to Muscalu. We also prove a non-commutative analogue of Cwikel’s theorem.

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References

  1. Bekjan, T.: Noncommutative Hardy space associated with semi-finite subdiagonal algebras. J. Math. Anal. Appl. 429(2), 1347–1369 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bennett, C., Sharpley, R.: Interpolation of Operators. Academic Press, New York (1988)

    MATH  Google Scholar 

  3. Cwikel, M.: K-divisibility of the K-functional and Calderón couples. Ark. Mat. 22, 39–62 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Davidson, K.: Nest Algebras. Pitmann Research Series (1988)

  5. Fack, T., Kosaki, H.: Generalised \(s\)-numbers of \(\tau \)-measurable operators. Pac. J. Math. 123, 269–300 (1986)

    Article  MATH  Google Scholar 

  6. Janson, S.: Interpolation of subcouples and quotient couples. Ark. Mat. 31(2), 307–338 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kaftal, V., Larson, D., Weiss, G.: Quasitriangular subalgebras of semifinite von Neumann algebras are closed. J. Funct. Anal. 107, 387–401 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kalton, N., Sukochev, F.: Symmetric norms and spaces of operators. J. Reine Angew. Math. 621, 81–121 (2008)

    MathSciNet  MATH  Google Scholar 

  9. Kisliakov, S.: Interpolation of \(H^p\)-spaces: some recent developments. Function spaces, interpolation spaces, and related topics (Haifa 1995), Israel Mathematica and conference proceedings . Bar-Ilan University, Ramat Gan 13, pp. 102–140 (1999)

  10. Krein, S., Petunin, Y., Semenov, E.: Interpolation of Linear Operators. American Mathematical Society, Providence (1982)

    Google Scholar 

  11. Lindenstrauss, J., Tzafiri, L.: Classical Banach Spaces, II edn. Springer, New York (1979)

    Book  Google Scholar 

  12. Lord, S., Sukochev, F., Zanin, D.: Singular Traces. Theory and Applications: De Gruyter Studies in Mathematics. De Gruyter, Berlin (2013)

    MATH  Google Scholar 

  13. Marsalli, M., West, G.: Noncommutative \(H_p\)-spaces. J. Oper. Theory 40, 339C–355C (1997)

    Google Scholar 

  14. Marsalli, M., West, G.: The dual of noncommutative \(H_1,\). Indiana Univ. Math. J. 47, 489C–500 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Muscalu, C.: A joint norm control Nehari type theorem for \(N\)-tuples of Hardy spaces. J. Geom. Anal. 9(4), 683–691 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pisier, G.: Interpolation between \(H^p\)-spaces and noncommutative generalization. Pac. J. Math. 155(2), 341–368 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  17. Pisier, G., Xu, Q.: Noncommutative \(L^p\)-spaces. In: Handbook of the Geometry of Banach Spaces. 2, 1459–1517 (2003)

  18. Power, S.: Factorization in analytic operator algebras. J. Funct. Anal. 67, 413–432 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  19. Randrianantoanina, N.: Hilbert transform associated with finite maximal subdiagonal algebras. Aust. Math. Soc. 65, 388C–404 (1999)

    Article  MathSciNet  Google Scholar 

  20. Sarason, D.: Generalised interpolation in \(H^{\infty }\). Trans. Am. Math. Soc. 127, 179–203 (1967)

    MATH  Google Scholar 

  21. Sukochev, F.: Completeness of quasi-normed symmetric operator spaces. Indag. Math. 25, 376–388 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Xu, Q.: Applications du théorème de factorisation pour des à fonctions o valeurs opératours. Studia Math. 95, 273–292 (1990)

    MathSciNet  Google Scholar 

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Correspondence to F. Sukochev.

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F. Sukochev and D. Zanin research is supported by the ARC.

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Sukochev, F., Tulenov, K. & Zanin, D. Nehari-Type Theorem for Non-commutative Hardy Spaces. J Geom Anal 27, 1789–1802 (2017). https://doi.org/10.1007/s12220-016-9740-9

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  • DOI: https://doi.org/10.1007/s12220-016-9740-9

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