A class of l 1 -preduals which are isomorphic to quotients of C ( ω ω )

Ioannis Gasparis

Studia Mathematica (1999)

  • Volume: 133, Issue: 2, page 131-143
  • ISSN: 0039-3223

Abstract

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For every countable ordinal α, we construct an l 1 -predual X α which is isometric to a subspace of C ( ω ω ω α + 2 ) and isomorphic to a quotient of C ( ω ω ) . However, X α is not isomorphic to a subspace of C ( ω ω α ) .

How to cite

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Gasparis, Ioannis. "A class of $l^1$-preduals which are isomorphic to quotients of $C(ω^ω)$." Studia Mathematica 133.2 (1999): 131-143. <http://eudml.org/doc/216609>.

@article{Gasparis1999,
author = {Gasparis, Ioannis},
journal = {Studia Mathematica},
keywords = {spaces of continuous functions; countable compact spaces; $l_1$-preduals; -spaces; compact interval of ordinals; order topology; countable compact metric space; -predual},
language = {eng},
number = {2},
pages = {131-143},
title = {A class of $l^1$-preduals which are isomorphic to quotients of $C(ω^ω)$},
url = {http://eudml.org/doc/216609},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Gasparis, Ioannis
TI - A class of $l^1$-preduals which are isomorphic to quotients of $C(ω^ω)$
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 2
SP - 131
EP - 143
LA - eng
KW - spaces of continuous functions; countable compact spaces; $l_1$-preduals; -spaces; compact interval of ordinals; order topology; countable compact metric space; -predual
UR - http://eudml.org/doc/216609
ER -

References

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  1. [1] D. E. Alspach, A quotient of C ( ω ω ) which is not isomorphic to a subspace of C(α), α < ω 1 , Israel J. Math. 33 (1980), 49-60. 
  2. [2] D. E. Alspach, A l 1 -predual which is not isometric to a quotient of C(α), in: Contemp. Math. 144, Amer. Math. Soc., 1993, 9-14. Zbl0796.46004
  3. [3] D. E. Alspach and Y. Benyamini, A geometrical property of C(K) spaces, Israel J. Math. 64 (1988), 179-194. Zbl0687.46013
  4. [4] Y. Benyamini, An extension theorem for separable Banach spaces, ibid. 29 (1978), 24-30. 
  5. [5] C. Bessaga and A. Pełczyński, Spaces of continuous functions IV, Studia Math. 19 (1960), 53-62. 
  6. [6] C. Bessaga and A. Pełczyński, On extreme points in separable conjugate spaces, Israel J. Math. 4 (1966), 262-264. Zbl0145.16102
  7. [7] I. Gasparis, Dissertation, The University of Texas, 1995. 
  8. [8] W. B. Johnson and M. Zippin, On subspaces of quotients of ( ∑ G n ) l p and ( ∑ G n ) c 0 , Israel J. Math. 13 (1972), 311-316. 
  9. [9] A. Lazar and J. Lindenstrauss, On Banach spaces whose duals are L 1 spaces and their representing matrices, Acta Math. 126 (1971), 165-194. Zbl0209.43201
  10. [10] S. Mazurkiewicz et W. Sierpiński, Contribution à la topologie des ensembles dénombrables, Fund. Math. 1 (1920), 17-27. Zbl47.0176.01
  11. [11] H. P. Rosenthal, On factors of C[0,1] with non-separable dual, Israel J. Math. 13 (1972), 361-378. 

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