Abstract
It is shown that every infinite-dimensional Banach space (resp., non-Schur space) (X,q) admits an equivalent norm p (resp., r) such that q ≦ p (resp., r ≦ q) and gap points do not exist between the q-sphere and p-sphere (resp., r-sphere) or their duals. The same conclusion is shown to hold in the case of the Schur space l1 in its usual norm.
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References
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© 1983 Springer-Verlag
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Lohman, R.H. (1983). On the existence of spheres and dual spheres without gap points. In: Pietsch, A., Popa, N., Singer, I. (eds) Banach Space Theory and its Applications. Lecture Notes in Mathematics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061567
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DOI: https://doi.org/10.1007/BFb0061567
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