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On the distance of non-reflexive spaces to the collection of all conjugate spaces

Published online by Cambridge University Press:  17 April 2009

Ivan Singer
Ivan Singer
Affiliation:
Institutul Naťional pentru Creaťie şti infˇifică ši Tehnică, Bucureˇti, Romania; Institutul de Matematica, Bucurešti, Romania.
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Abstract

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We show that there exists a conjugate Banach space E = B* with a basis, such that the distance from E to the collection of all conjugate Banach spaces can be made arbitrarily large, by suitable renorming of E. This solves a problem raised by B.V. Godun, Dokl. Akad. Nauk SSSR. 236 (1977), 18–20.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 3 , June 1978 , pp. 461 - 464
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Davis, William J. and Johnson, William B., “A renorming of nonreflexive Banach spaces”, Proc. Amer. Math. Soc. 37 (1973), 486–488.CrossRefGoogle Scholar
[2]Dulst, Dick van and Singer, Ivan, “On Kadec-Klee norms on Banach spaces”, Studia Math. 54 (1975–1976), 205–211.CrossRefGoogle Scholar
[3]Enflo, Per, “A counterexample to the approximation problem in Banach spaces“, Acta Math. 130 (1973), 309–317.CrossRefGoogle Scholar
[4]Figiel, T. and Johnson, W.B., “The approximation property does not imply the bounded approximation property”, Proc. Amer. Math. Soc. 41 (1973), 197–200.CrossRefGoogle Scholar
[5]ΓΟдуН, Б.Β. [Godun, B.V.], “зНΗΒизΒaлeзx0344;зыe зHoρMы Ha HeρeøлeHCиBHыX ⊡ρocTρaHCTBax“ [Equivalent norms on nonreflexive spaces], Dokl. Akad. Nauk SSSR. 236 (1977), 18–20.Google Scholar
[6]Grothendieck, Alexandre, Produits tensoriels topologiques et espaces nucléaires (Memoirs Amer. Math. Soc. 16. American Mathematical Society, Providence, Rhode Island, 1955).Google Scholar
[7]Johnson, W.B., Rosenthal, H.P. and Zippin, M., “On basis, finite dimensional decompositions and weaker structures in Banach spaces“, Israel J. Math. 9 (1971), 488–506.Google Scholar
[8]Lindenstrauss, Joram, “On James's paper ‘Separable conjugate spaces’”, Israel J. Math. 9 (1971), 279–284.CrossRefGoogle Scholar