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A note on bump functions that locally depend on finitely many coordinates

  • M. Fabian (a1) and V. Zizler (a2)

Abstract

We show that if a continuous bump function on a Banach space X locally depends on finitely many elements of a set F in X*, then the norm closed linear span of F equals to X*. Some corollaries for Markuševič bases and Asplund spaces are derived.

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Copyright

References

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[1]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64 (Longman, Harlow, 1993).
[2]Habala, P., Hájek, P. and Zizler, V., Introduction to Banach spaces I, II, (Lecture Notes) (Matfyzpress, Charles University, Prague, 1996).
[3]Hájek, P., ‘Smooth norms that depend locally on finitely many coordinates’, Proc. Amer. Math. Soc. 123 (1995), 38173821.
[4]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I, Sequence spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1977).
[5]Pechanec, J., Whitfield, J.H.M. and Zizler, V., ‘Norms locally dependent on finitely many coordinates’, An. Acad. Brasil. Ciênc. 53 (1981), 415417.
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A note on bump functions that locally depend on finitely many coordinates

  • M. Fabian (a1) and V. Zizler (a2)

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