DOI QR코드

DOI QR Code

SEPARABLE REFLEXIVE BANACH SUBLATTICES OF WeakL1

  • 투고 : 2013.04.16
  • 심사 : 2013.07.16
  • 발행 : 2013.08.15

초록

We investigate complemented Banach sublattices of the Banach envelope of $WeakL^1$. In particular, the Banach envelope of $WeakL^1$ contains a complemented Banach sublattice that is isometrically isomorphic to a separable reflexive Banach lattice.

키워드

참고문헌

  1. M. Cwikel and Y. Sagher, L(p,${\infty}$)*, Indiana Uni. Math. J. 21 (1972), 782-786.
  2. M. Cwikel, On the conjugates of some function spaces, Studia Math. 45 (1973), 49-55. https://doi.org/10.4064/sm-45-1-49-55
  3. M. Cwikel and C. Fefferman, Maximal seminorm on $WeakL^1$, Studia Math. 69 (1980), 149-154.
  4. M. Cwikel and C. Fefferman, The canonical seminorm on $WeakL^1$, Studia Math. 78 (1984), 275-278. https://doi.org/10.4064/sm-78-3-275-278
  5. N. Dunford and J. T. Schwartz, Linear Operator I : General Theory. Pure and Applied Mathematics, New York: Interscience VII, 1967.
  6. J. Kang, Banach subspaces and envelope norm of $wL_i$, Bull. Korean. Math. Soc. 35 (1998), 409-420.
  7. J. Kupka and T. Peck, The $L_1$-structure of $WeakL^1$, Math. Ann. 269 (1984), 235-262. https://doi.org/10.1007/BF01451421
  8. Lindenstrauss and Tzafriri, Classical Banach Spaces II, Springer-Verlag, New York, 1974.
  9. H. P. Lotz and T. Peck, Sublattices of the Banach envelope of $WeakL^1$, Proc. Amer. Math. Soc. 126 (1998), 75-84.
  10. T. Peck and M. Talagrand, Banach sublattices of $WeakL^1$, Israel. J. Math. 59 (1987), 257-271. https://doi.org/10.1007/BF02774140