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A banach space containing non-trivial limited sets but no non-trivial bounding sets

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Abstract

An example of a Banach spaceE is given with the following properties: Every bounding setA⊂E (i.e.f(A) is bounded for each holomorphic functionf:E →C) is relatively compact but there are relatively non-compact limited setsA (i.e.T(A) is relatively compact for each bounded linear mapT:E →c 0).

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References

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  2. S. Dineen,Complex analysis in locally convex spaces, North-Holland Studies57 (1981).

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  5. B. Josefson,Bounding subsets of l ∞ (A), J. Math. Pures Appl.57 (1978).

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  1. Department of Mathematics, University of Linköping, S-581 83, Linköping, Sweden

    Bengt Josefson

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  1. Bengt Josefson
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Josefson, B. A banach space containing non-trivial limited sets but no non-trivial bounding sets. Israel J. Math. 71, 321–327 (1990). https://doi.org/10.1007/BF02773750

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  • DOI: https://doi.org/10.1007/BF02773750

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