A lifting theorem for locally convex subspaces of L 0

R. Faber

Studia Mathematica (1995)

  • Volume: 115, Issue: 1, page 73-85
  • ISSN: 0039-3223

Abstract

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We prove that for every closed locally convex subspace E of L 0 and for any continuous linear operator T from L 0 to L 0 / E there is a continuous linear operator S from L 0 to L 0 such that T = QS where Q is the quotient map from L 0 to L 0 / E .

How to cite

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Faber, R.. "A lifting theorem for locally convex subspaces of $L_0$." Studia Mathematica 115.1 (1995): 73-85. <http://eudml.org/doc/216199>.

@article{Faber1995,
abstract = {We prove that for every closed locally convex subspace E of $L_0$ and for any continuous linear operator T from $L_0$ to $L_0/E$ there is a continuous linear operator S from $L_0$ to $L_0$ such that T = QS where Q is the quotient map from $L_0$ to $L_0/E$.},
author = {Faber, R.},
journal = {Studia Mathematica},
keywords = {lifting theorem},
language = {eng},
number = {1},
pages = {73-85},
title = {A lifting theorem for locally convex subspaces of $L_0$},
url = {http://eudml.org/doc/216199},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Faber, R.
TI - A lifting theorem for locally convex subspaces of $L_0$
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 1
SP - 73
EP - 85
AB - We prove that for every closed locally convex subspace E of $L_0$ and for any continuous linear operator T from $L_0$ to $L_0/E$ there is a continuous linear operator S from $L_0$ to $L_0$ such that T = QS where Q is the quotient map from $L_0$ to $L_0/E$.
LA - eng
KW - lifting theorem
UR - http://eudml.org/doc/216199
ER -

References

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  1. [1] T. Aoki, Locally bounded linear topological spaces, Proc. Imp. Acad. Tokyo 18 (1942), No. 10 Zbl0060.26503
  2. [2] N. J. Kalton and N. T. Peck, Quotients of L p for 0≤ p<1, Studia Math. 64 (1979), 65-75. Zbl0393.46007
  3. [3] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, Cambridge Univ. Press, Cambridge, 1984. 
  4. [4] S. Kwapień, On the form of a linear operator in the space of all measurable functions, Bull. Acad. Polon. Sci. 21 (1973), 951-954. Zbl0271.60004
  5. [5] R. E. A. C. Paley and A. Zygmund, On some series of functions III, Proc. Cambridge Philos. Soc. 28 (1932), 190-205. Zbl0006.19802
  6. [6] N. T. Peck and T. Starbird, L 0 is ω-transitive, Proc. Amer. Math. Soc. 83 (1981), 700-704. 
  7. [7] S. Rolewicz, On a certain class of linear metric spaces, Bull. Acad. Polon. Sci. 5 (1957), 471-473. Zbl0079.12602
  8. [8] P. Turpin, Convexités dans les espaces vectoriels topologiques généraux, Dissertationes Math. 131 (1976). 

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