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Planar Faces of Operator Spaces in L P

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Topics in Matrix and Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 50))

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Abstract

The following statement was proved in [1], Let 1 < P < ∞ and let M p be the multiplier space in L p spaces with respect to the exponent system.

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References

  1. Fefferman, C. and H. Shapiro: A planar face on the unit sphere of the multiplier space M p, 1 < p < ∞. Proc. Amer. Math. Soc., 36, (1972), 435–439.

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  2. Benyamini, Y. and Pei-Kee Lin: Norm one multipliers on L p(G). Arkiv for matematik, 24, (1986), 159–173.

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  3. Semenov, E.M. and I. Ya. Shneiberg: Geometrical properties of a unit sphere of the operator space L p. The Gohberg Anniversary Collection. Vol. I. Operator Theory: Advances and Application. Vol. 41 (1988), 497–510.

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  4. Semenov, E.M. and I. Ya. Shneiberg: Hypercontracting operators and Khintchine’s inequality. Funct. Anal, and its Appl. 22, (1988), 87–88 (Russian).

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  5. Diestel, J.: Geometry of Banach Spaces. Springer, Berlin-Heidelberg-New York (1975).

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  6. Hardy, G.H., J.E. Littlewood and G. Polya: Inequalities. Cambridge University Press, Cambridge (1934).

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  7. Benyamini, Y. and Pei-Kee Lin: An operator on L p without best compact approximation. Israel J, Math. 51, (1985), 298–304.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Voronezh State University, Voronezh, 394693, USSR

    E. M. Semenov

  2. Voronezh Forest Technology Institute, Voronezh, 394043, USSR

    I. Ya. Shneiberg

Authors
  1. E. M. Semenov
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  2. I. Ya. Shneiberg
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Editor information

Editors and Affiliations

  1. Econometric Institute, Erasmus University Rotterdam, Postbus 1738, 3000 DR, Rotterdam, The Netherlands

    H. Bart , I. Gohberg  & M. A. Kaashoek ,  & 

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© 1991 Springer Basel AG

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Semenov, E.M., Shneiberg, I.Y. (1991). Planar Faces of Operator Spaces in L P . In: Bart, H., Gohberg, I., Kaashoek, M.A. (eds) Topics in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 50. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5672-0_14

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  • DOI: https://doi.org/10.1007/978-3-0348-5672-0_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5674-4

  • Online ISBN: 978-3-0348-5672-0

  • eBook Packages: Springer Book Archive

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