Rocky Mountain Journal of Mathematics

On Properties of $M$-Ideals

Juan Carlos Cabello and Eduardo Nieto

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 28, Number 1 (1998), 61-93.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181071823

Digital Object Identifier
doi:10.1216/rmjm/1181071823

Mathematical Reviews number (MathSciNet)
MR1639829

Zentralblatt MATH identifier
0936.46014

Citation

Cabello, Juan Carlos; Nieto, Eduardo. On Properties of $M$-Ideals. Rocky Mountain J. Math. 28 (1998), no. 1, 61--93. doi:10.1216/rmjm/1181071823. https://projecteuclid.org/euclid.rmjm/1181071823


Export citation

References

  • E.M. Alfsen and E.G. Effros, Structure in real Banach spaces, Part I and II, Ann. of Math. 96 (1972), 98-173.
  • T. Ando, Closed range theorems for convex sets and linear liftings, Pacific J. Math. 44 (1973), 393-410.
  • C.-M. Cho and W.B. Johnson, A characterization of subspaces $X$ of $l_p$ for which $\K(X)$ is an $M$-ideal in $\L(X)$, Proc. Amer. Math. Soc. 93 (1985), 466-470.
  • W.J. Davis and R.R. Phelps, The Radon-Nikodým property and dentables sets in Banach spaces, Proc. Amer. Math. Soc. 45 (1974), 119-122.
  • J. Diestel, Geometry of Banach spaces\emdash/Selected topics, Lecture Notes in Math. 485, Springer, New York, 1975.
  • J. Diestel and J.J. Uhl, Vector measures, Math. Surveys 15, American Mathematical Soceity, Providence, Rhode Island, 1977.
  • D. Van Dulst, Reflexive and superreflexive Banach spaces, Math. Centre Tracts 102, Amsterdam, 1978.
  • M. Fabian and G. Godefroy, The dual of every Asplund space admits a projectional resolution of the identity, Studia Math. 91 (1988), 141-151.
  • G. Godefroy and N.J. Kalton, The ball topology and its applications, Contemp. Math. 85 (1989), 195-237.
  • G. Godefroy, N.J. Kalton and P.D. Saphar, Unconditional ideals in Banach spaces, Studia Math. 104 (1993), 13-59.
  • G. Godefroy and D. Li, Banach spaces which are $M$-ideals in their bidual have property $(u)$, Ann. Inst. Fourier 39 (1989), 361-371.
  • G. Godefroy and P. Saab, Weakly unconditionally convergent series in $M$-ideals, Math. Scand. 64 (1989), 307-318.
  • G. Godefroy and D. Saphar, Duality in spaces of operators and smooth norms in Banach spaces, Illinois J. Math. 32 (1988), 672-695.
  • P. Harmand and A. Lima, Banach spaces which are $M$-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1984), 253-264.
  • P. Harmand, D. Werner and W. Werner, $M$-ideals in Banach spaces and \nBanach, algebras, Lecture Notes in Math. 1547, Springer, New York, 1993.
  • J. Hennefeld, $M$-ideals, $HB$-subspaces, and compact operators, Indiana Univ. Math. J. 28 (1979), 927-934.
  • J. Johnson and J. Wolfe, On the norm of the canonical projection of $E^***$ onto $E^\perp$, Proc. Amer. Math. Soc. 75 (1979), 50-52.
  • N.J. Kalton, $M$-ideals of compact operators, Illinois J. Math. 37 (1993), 147-169.
  • Å. Lima, Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1-62.
  • --------, On $M$-ideals and best approximation, Indiana Univ. Math. J. 31 (1982), 27-36.
  • Å. Lima, E. Oja, T.S.S.R.K. Rao and D. Werner, Geometry of operator spaces, Michigan Math. J. 41 (1994), 473-490.
  • J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Springer, New York, 1977.
  • E. Oja, On the uniqueness of the norm-preserving extension of a linear functional in the Hahn-Banach theorem, Izv. Akad. Nauk Est. SSR 33 (1984), 424-438 (Russian).
  • E. Oja, Strong uniqueness of the extension of linear continuous functionals according to the Hahn-Banach theorem, Math. Notes 43 (1988), 134-139.
  • R.R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238-255.
  • M.A. Smith and Sullivan, Extremely smooth Banach spaces, in Banach spaces of analytic functions, Lecture Notes in Math. 604, 125-137. Springer, New York, 1977.
  • D. Werner, New classes of Banach spaces which are $M$-ideals in their biduals, Math. Proc. Cambridge Phil. Soc. 111 (1992), 337-354.
  • D. Werner, $M$-ideals and the `basic inequality', J. Approx. Theory 76 (1994), 21-30.