Abstract
It is shown tat, for 1 <p < 2, there is an uncomplemented subspace ofL p [0,1] that is isomorphic to Hilbert space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Bennett, V. Goodman and C. M. Newman,Norms of random matrices, Pacific J. Math.59 (1975), 359–365.
L. E. Dor, On projections in L1, Ann. of Math.102 (1975), 463–474.
A. Dvoretsky,Some results on convex bodies and Banach spaces, Proc. Symp. on Linear Spaces, Jerusalem, 1961, 123–174.
T. Figiel, J. Lindenstrauss and V. D. Milman,The dimension of almost spherical sections of convex bodies, to appear.
J. Khinchine,Über die Diadischen Brüche, Math. Z.18 (1923), 109–116.
V. D. Milman,A new proof of Dvoretzky’s theorem on sections of convex bodies, Functional Anal. Appl.5 (1971), 28–37 (Russian).
W. Orlicz,Über unbedingte Konvergenz in Funktionenräumen (I), Studia Math.4 (1933), 33–37.
A. Pelczynski,Projections in certain Banach spaces, Studia Math.19 (1960), 209–228.
A. Pelczynski and H. P. Rosenthal,Localization techniques in L p spaces, Studia Math.52 (1975), 263–289.
C. A. Rogers,Covering a sphere with spheres, Mathematika10 (1963), 157–164.
H. P. Rosenthal,Projections onto translation invariant subspaces of L P (G), Mem. Amer. Math. Soc.63 (1966).
H. P. Rosenthal,On the subspaces of L p (p > 2)spanned by sequences of independent random variables, Israel J. Math.8 (1970), 273–303.
W. Rudin,Trigonometric series with gaps, J. Math. Mech.9 (1960), 203–227.
Author information
Authors and Affiliations
Additional information
Supported in part by NSF MPS 75-07390
Supported in part by NSF MSP 72-04634
Supported in part by NSF MSP 73-08715
Supported in part by NSF MSP 74-04870 A01
Rights and permissions
About this article
Cite this article
Bennett, G., Dor, L.E., Goodman, V. et al. On uncomplemented subspaces ofL p , 1 <p <2. Israel J. Math. 26, 178–187 (1977). https://doi.org/10.1007/BF03007667
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03007667