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The iterated weak Hilbert procedure

Authors: Martin Defant and Marius Junge
Journal: Proc. Amer. Math. Soc. 117 (1993), 645-651
MSC: Primary 46A32; Secondary 46C99, 47D50
MathSciNet review: 1152274
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Abstract: Applying Pisier's concept of weak properties to weak Hilbert spaces we obtain the so-called weak weak Hilbert spaces. Our main result is that the classes of weak Hilbert spaces and of weak weak Hilbert spaces coincide. On the other hand we show that a generalization for operators does not hold.

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  • [DJ] Martin Defant and Marius Junge, On weak (𝑟,2)-summing operators and weak Hilbert spaces, Studia Math. 96 (1990), no. 3, 203–217. MR 1067307
  • [Jo] Fritz John, Extremum problems with inequalities as subsidiary conditions, Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience Publishers, Inc., New York, N. Y., 1948, pp. 187–204. MR 0030135
  • [K] S. Kwapień, A linear topological characterization of inner-product spaces, Studia Math. 38 (1970), 277–278. MR 0276738
  • [P1] A. Pietsch, Eigenvalues and 𝑠-numbers, Mathematik und ihre Anwendungen in Physik und Technik [Mathematics and its Applications in Physics and Technology], vol. 43, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987. MR 917067
    Albrecht Pietsch, Eigenvalues and 𝑠-numbers, Cambridge Studies in Advanced Mathematics, vol. 13, Cambridge University Press, Cambridge, 1987. MR 890520
  • [P2] Albrecht Pietsch, Operator ideals, North-Holland Mathematical Library, vol. 20, North-Holland Publishing Co., Amsterdam-New York, 1980. Translated from German by the author. MR 582655
  • [Pi1] Gilles Pisier, Weak Hilbert spaces, Proc. London Math. Soc. (3) 56 (1988), no. 3, 547–579. MR 931514,
  • [Pi2] Gilles Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989. MR 1036275
  • [T-J] Nicole Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 993774

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Keywords: Weak Hilbert spaces, weak weak Hilbert spaces
Article copyright: © Copyright 1993 American Mathematical Society