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Contractive projections in nonatomic function spaces

Author: Beata Randrianantoanina
Journal: Proc. Amer. Math. Soc. 123 (1995), 1747-1750
MSC: Primary 46E30; Secondary 46B20
MathSciNet review: 1273518
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Abstract: We prove that there are no 1-complemented subspaces of finite codimension in separable rearrangement-invariant nonatomic function spaces not isometric to $ {L_2}$.

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  • [1] Dan Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications, vol. 20, Birkhäuser Verlag, Basel, 1986. MR 897527
  • [2] Bernard Beauzamy and Bernard Maurey, Points minimaux et ensembles optimaux dans les espaces de Banach, J. Functional Analysis 24 (1977), no. 2, 107–139. MR 0428014
  • [3] E. W. Cheney and K. H. Price, Minimal projections, Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press, London, 1970, pp. 261–289. MR 0265842
  • [4] R. G. Douglas, Contractive projections on an 𝔏₁ space, Pacific J. Math. 15 (1965), 443–462. MR 0187087
  • [5] D. G. de Figueiredo and L. A. Karlovitz, On the extension of contractions on normed spaces, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 95–104. MR 0275120
  • [6] P. Harmand, D. Werner, and W. Werner, 𝑀-ideals in Banach spaces and Banach algebras, Lecture Notes in Mathematics, vol. 1547, Springer-Verlag, Berlin, 1993. MR 1238713
  • [7] N. J. Kalton and Beata Randrianantoanina, Surjective isometries on rearrangement-invariant spaces, Quart. J. Math. Oxford Ser. (2) 45 (1994), no. 179, 301–327. MR 1295579, 10.1093/qmath/45.3.301
  • [8] Nigel J. Kalton and Beata Randrianantoanina, Isometries on rearrangement-invariant spaces, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 4, 351–355 (English, with English and French summaries). MR 1204303, 10.1093/qmath/45.3.301
  • [9] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367
  • [10] B. Randrianantoanina, Isometries of function spaces, Ph.D. Dissertation, University of Missouri-Columbia, 1993.
  • [11] Haskell Rosenthal, Contractively complemented subspaces of Banach spaces with reverse monotone (transfinite) bases, Texas functional analysis seminar 1984–1985 (Austin, Tex.), Longhorn Notes, Univ. Texas Press, Austin, TX, 1985, pp. 1–14. MR 832246
  • [12] Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
  • [13] D. E. Wulbert, Projections of norm 1 on $ C(X)$, Notices Amer. Math. Soc. 15 (1968), 362.

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