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    Haller, Rainis Johanson, Marje and Oja, Eve 2012. M(r, s)-ideals of compact operators. Czechoslovak Mathematical Journal, Vol. 62, Issue. 3, p. 673.

    Abrahamsen, Trond A. Lima, Åsvald and Lima, Vegard 2008. Unconditional ideals of finite rank operators. Czechoslovak Mathematical Journal, Vol. 58, Issue. 4, p. 1257.

    Oja, Eve and Põldvere, Märt 2007. Norm-preserving extensions of functionals and denting points of convex sets. Mathematische Zeitschrift, Vol. 258, Issue. 2, p. 333.

    Lima, Åsvald and Oja, Eve 2004. Ideals of compact operators. Journal of the Australian Mathematical Society, Vol. 77, Issue. 01, p. 91.

    Oja, E. and Põldvere, M. 1999. Intersection properties of ball sequences and uniqueness of Hahn–Banach extensions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 129, Issue. 06, p. 1251.

    Cabello, Juan Carlos Nieto, Eduardo and Oja, Eve 1998. On Ideals of Compact Operators Satisfying theM(r,s)-Inequality. Journal of Mathematical Analysis and Applications, Vol. 220, Issue. 1, p. 334.


HB-subspaces and Godun sets of subspaces in Banach spaces

  • Eve Oja (a1)
  • DOI:
  • Published online: 01 February 2010

Let X be a Banach space and Y its closed subspace having property U in X. We use a net (Aα) of continuous linear operators on X such that ‖ Aα ‖ ≤ 1, Aα (X) ⊂ Y for all α, and limαg(Aαy) = g(y), yY, gY* to obtain equivalent conditions for Y to be an HB-subspace, u-ideal or h-ideal of X. Some equivalent renormings of c0 and l2 are shown to provide examples of spaces X for which K(X) has property U in L(X) without being an HB-subspace. Considering a generalization of the Godun set [3], we establish some relations between Godun sets of Banach spaces and related operator spaces. This enables us to prove e.g., that if K(X) is an HB-subspace of L(X), then X is an HB-subspace of X**—the result conjectured to be true by Å. Lima [9].

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5.J. Hennefeld . M-ideals, HB-subspaces, and compact operators. Indiana Univ. Math. J., 28 (1979), 927934.

6.J. Johnson . Remarks on Banach spaces of compact operators. J. Fund. Anal., 32 (1979), 304311.

7.J. Johnson and J. Wolfe . On the norm of the canonical projection of E*** onto E1. Proc. Amer. Math. Soc., 75 (1979), 5052.

8.A. Lima . On M-ideals and best approximation. Indiana Univ. Math. J., 31 (1982), 2736.

12.J. Lindenstrauss and L. Tzafriri . On the complemented subspaces problem. Israel J. Math., 9 (1971), 263269.

17.R. R. Phelps . Uniqueness of Hahn-Banach extensions and unique best approximation. Trans Amer. Math. Soc., 95 (1960), 238255.

18.I. Singer . Bases in Banach spaces, Vol. 2 (Springer-Verlag, 1981).

20.A. E. Taylor . The extension oflinear functionals. Duke Math. J., 5 (1939), 538547.

21.D. Yost . Approximation by compact operators between C(X) spaces. J. Approx. Th., 49 (1987), 99109.

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